Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological algebraic structures, and provides more than 600 current references and 570 display equations for further exploration of the topic. It provides stimulating discussions from world-renowned names including Laszlo Fuchs, Robert Gilmer, Saharon Shelah, Daniel Simson, and Richard Swan to celebrate 40 years of study on cumulative rings. Describing emerging theories

This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis.
All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains.
Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more
Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.

Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.

This volume showcases mostly the contributions presented at the International Conference in Algebra and Its Applications held at the Aligarh Muslim University, Aligarh, India during November 12-14, 2016. Refereed by renowned experts in the field, this wide-ranging collection of works presents the state of the art in the field of algebra and its applications covering topics such as derivations in rings, category theory, Baer module theory, coding theory, graph theory, semi-group theory, HNP rings, Leavitt path algebras, generalized matrix algebras, Nakayama conjecture, near ring theory and lattice theory. All of the contributing authors are leading international academicians and researchers in their respective fields. Contents On Structure of -Prime Rings with Generalized Derivation A characterization of additive mappings in rings with involution| Skew constacyclic codes over Fq + vFq + v2Fq Generalized total graphs of commutative rings: A survey Differential conditions for which near-rings are commutative rings Generalized Skew Derivations satisfying the second Posner's theorem on Lie ideals Generalized Skew-Derivations on Lie Ideals in Prime Rings On generalized derivations and commutativity of prime rings with involution On (n, d)-Krull property in amalgamated algebra Pure ideals in ordered -semigroups Projective ideals of differential polynomial rings over HNP rings Additive central m-power skew-commuting maps on semiprime rings A Note on CESS-Lattices Properties Inherited by Direct Sums of Copies of a Module Modules witnessing that a Leavitt path algebra is directly infinite Inductive Groupoids and Normal Categories of Regular Semigroups Actions of generalized derivations in Rings and Banach Algebras Proper Categories and Their Duals On Nakayama Conjecture and related conjectures-Review On construction of global actions for partial actions On 2-absorbing and Weakly 2-absorbing Ideals in Product Lattices Separability in algebra and category theory Annihilators of power values of generalized skew derivations on Lie ideals Generalized derivations on prime rings with involution

Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its desirable properties. This book gathers together for the first time in one place recent work on extending modules. It is aimed at anyone with a basic knowledge of ring and module theory.

The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.

This popular textbook was thoughtfully and specifically tailored to introducing undergraduate students to linear algebra. The second edition has been carefully revised to improve upon its already successful format and approach. In particular, the author added a chapter on quadratic forms, making this one of the most comprehensive introductory texts on linear algebra.

This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.

The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts.

"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."

The book reports a comparative research project about algebra teaching and learning in four countries. Algebra is a central topic of learning across the world, and it is well-known that it represents a hurdle for many students. The book presents analyses built on extensive video-recordings of classrooms documenting the first introduction to symbolic algebra (students aged 12 to 14). While the content addressed in all classrooms is variables, expressions and equations, the teaching approaches are diverse. The chapters bring the reader into different algebra classrooms, discussing issues such as mathematization and social norms, the role of mediating tools and designed examples, and teacher beliefs. By comparing classrooms, new insights are generated about how students understand the algebraic content, how teachers instruct, and how both parties deal with difficulties in learning elementary algebra. The book also describes a research methodology using video in search of taken-for-granted aspects of algebra lessons.

This is the first book to systematically study the weak systems of mereology. In its chapters, the author critically analyzes and explains core topics related to mereology, such as parthood without antisymmetry, non-existence of the zero element, and Lesniewski's notion of class and set. The book also delves into three theories of parthood: two concern the sum existence axioms, and the third contends with transitivity of parthood. This is the first systematic analysis of systems of mereology of its kind and is suitable for students, scholars, logicians, and mathematicians who wish to further their knowledge of mereology. Original polish publication "Podstawy teorii czesci" by The Nicolaus Copernicus University Press

Group testing was first proposed for blood tests, but soon found its way to many industrial applications. Combinatorial group testing studies the combinatorial aspect of the problem and is particularly related to many topics in combinatorics, computer science and operations research. Recently, the idea of combinatorial group testing has been applied to experimental designs, coding, multiaccess computer communication, clone library screening and other fields. This book is the first attempt to cover the theory and applications of combinatorial group testing in one place.

" Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more "

Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.

About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visi

This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry), including a chapter on finite subgroups of 0 (2). Each of the 23 chapters concludes with a generous helping of exercises, and a selection of these have solutions at the end of the book. The chapters also contain many examples, both numerical worked examples (mostly in 2 and 3 dimensions), as well as examples which take some of the ideas further. Many of the chapters contain "complements" which develop more special topics, and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course, either by omitting whole chapters or by omitting the "complements" or specific examples.

This volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines.

In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts.

The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus.

This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.

Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, analytic and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum contains refereed contributions on: general problems of diophantine approximation; quadratic forms and their connections with automorphic forms; the modular group and its subgroups; continued fractions; hyperbolic geometry; and the lower part of the Markoff spectrum.;Written by over 30 authorities in the field, this book should be a useful resource for research mathematicians in harmonic analysis, number theory algebra, geometry and probability and graduate students in these disciplines.

This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.

An important question in geometry and analysis is to know when two "k"-forms "f "and g are equivalent through a change of variables. The problem is therefore to find a map " "so that it satisfies the pullback equation: " ""*"("g") = "f."

In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases "k "= 2 and "k "= "n," but much less when 3 "k " "n"-1. The present monograph provides thefirst comprehensive study of the equation.

The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge-Morrey decomposition and to give several versions of the Poincare lemma. The core of the book discusses the case "k "= "n," and then the case 1 "k " "n"-1 with special attention on the case "k "= 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Holder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Holder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation.

"The Pullback Equation for Differential Forms "is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars."