Kasch Modules.- Compactness in Categories and Interpretations.- A Ring of Morita Context in Which Each Right Ideal is Weakly Self-injective.- Splitting Theorems and a Problem of Muller.- Decompositions of D1 Modules.- Right Cones in Groups.- On Extensions of Regular Rings of Finite Index by Central Elements.- Intersections of Modules.- Minimal Cogenerators Over Osofsky and Camillo Rings.- Uniform Modules Over Goldie Prime Serial Rings.- Co-Versus Contravariant Finiteness of Categories of Representations.- Monomials and the Lexicographic Order.- Rings Over Which Direct Sums of CS Modules Are CS.- Exchange Properties and the Total.- Local Bijective Gabriel Correspondence and Torsion Theoretic FBN Rings.- Normalizing Extensions and the Second Layer Condition.- Generators of Subgroups of Finite Index in GLm (?G).- Weak Relative Injective M-Subgenerated Modules.- Direct Product and Power Series Formations Over 2-Primal Rings.- Localization in Noetherian Rings.- Projective Dimension of Ideals in Von Neumann Regular Rings.- Homological Properties of Color Lie Superalgebras.- Indecomposable Modules Over Artinian Right Serial Rings.- Nonsingular Extending Modules.- Right Hereditary, Right Perfect Rings Are Semiprimary.- On the Endomorphism Ring of a Discrete Module: A Theorem of F. Kasch.- Nonsingular Rings with Finite Type Dimension.

This book discusses the revolution of cycles and rhythms that is expected to take place in different branches of science and engineering in the 21st century, with a focus on communication and information processing. It presents high-quality papers in vibration sciences, rhythms and oscillations, neurosciences, mathematical sciences, and communication. It includes major topics in engineering and structural mechanics, computer sciences, biophysics and biomathematics, as well as other related fields. Offering valuable insights, it also inspires researchers to work in these fields. The papers included in this book were presented at the 1st International Conference on Engineering Vibration, Communication and Information Processing (ICoEVCI-2018), India.

An increasing variety of biological problems involving resource management, conservation and environmental quality have been dealt with using the principles of population biology (defined to include population dynamics, genetics and certain aspects of community ecology). There appears to be a mixed record of successes and failures and almost no critical synthesis or reviews that have attempted to discuss the reasons and ways in which population biology, with its remarkable theoretical as well as experimental advances, could find more useful application in agriculture, forestry, fishery, medicine and resource and environmental management. This book provides examples of state-of-the-art applications by a distinguished group of researchers in several fields. The diversity of topics richly illustrates the scientific and economic breadth of their discussions as well as epistemological and comparative analyses by the authors and editors. Several principles and common themes are emphasized and both strengths and potential sources of uncertainty in applications are discussed. This volume will hopefully stimulate new interdisciplinary avenues of problem-solving research.

Geomicrobiology is a combination of geology and microbiology, and includes the study of interaction of microorganisms with their environment, such as in sedimentary rocks. This is a new and rapidly-developing field that has led in the past decade to a radically-revised view of the diversity and activity of microbial life on Earth. Geomicrobiology examines the role that microbes have played in the past and are currently playing in a number of fundamental geological processes. The present book is of great importance for researchers working in the field of microbiology, biotechnology, geology and environmental biotechnology. It can be a major reference book for students as well as researchers.

Geomicrobiology is a combination of geology and microbiology, and includes the study of interaction of microorganisms with their environment, such as in sedimentary rocks. This is a new and rapidly-developing field that has led in the past decade to a radically-revised view of the diversity and activity of microbial life on Earth. Geomicrobiology examines the role that microbes have played in the past and are currently playing in a number of fundamental geological processes. The present book is of great importance for researchers working in the field of microbiology, biotechnology, geology and environmental biotechnology. It can be a major reference book for students as well as researchers.

An increasing variety of biological problems involving resource management, conservation and environmental quality have been dealt with using the principles of population biology (defined to include population dynamics, genetics and certain aspects of community ecology). There appears to be a mixed record of successes and failures and almost no critical synthesis or reviews that have attempted to discuss the reasons and ways in which population biology, with its remarkable theoretical as well as experimental advances, could find more useful application in agriculture, forestry, fishery, medicine and resource and environmental management. This book provides examples of state-of-the-art applications by a distinguished group of researchers in several fields. The diversity of topics richly illustrates the scientific and economic breadth of their discussions as well as epistemological and comparative analyses by the authors and editors. Several principles and common themes are emphasized and both strengths and potential sources of uncertainty in applications are discussed. This volume will hopefully stimulate new interdisciplinary avenues of problem-solving research.

It follows naturally from the widely accepted Darwinian dictum that failures of populations or of species to adapt and to evolve under changing environments will result in their extinction. Population geneti cists have proclaimed a centerstage role in developing conservation biology theory and applications. However, we must critically reexamine what we know and how we can make rational contributions. We ask: Is genetic variation really important for the persistence of species? Has any species become extinct because it ran out of genetic variation or because of inbreeding depression? Are demographic and environmental stochas ticity by far more important for the fate of a population or species than genetic stochasticity (genetic drift and inbreeding)? Is there more to genetics than being a tool for assessing reproductive units and migration rates? Does conventional wisdom on inbreeding and "magic numbers" or rules of thumb on critical effective population sizes (MVP estimators) reflect any useful guidelines in conservation biology? What messages or guidelines from genetics can we reliably provide to those that work with conservation in practice? Is empirical work on numerous threatened habitats and taxa gathering population genetic information that we can use to test these guidelines? These and other questions were raised in the invitation to a symposium on conservation genetics held in May 1993 in pleasant surroundings at an old manor house in southern Jutland, Denmark."

This volume is an outcomeof invited lecturesdelivered at the Ring Theory Section of the 23rd Ohio State-DenisonConferencein May 1996. It also contains articles by some invited mathematicianswho could not attend the conference. These peer-refereedarticles showcasethe latest developmentsand trends in classicalRing Theory, highlighting the cro- fertilization of new techniquesand ideaswith the existing ones. Providing a wide variety of methodologies,this volume should be valuable both to graduatestudentsas well as to specialistsin Ring Theory. We would like to thank our colleagueswho investeda lot of their time to make the conferencea great success. In particular, our thanks go to ProfessorsTom Dowling, Dan Sanders,SurinderSehgal,Ron Solomonand Sergio R. L6pez-Permouthfor their help. The financial support for the Conference,provided by the Departmentof Mathematics,The Ohio State University, and MathematicsResearchInstitute, Columbus, is gratefully acknowleged. Many thanksgo to Dean Violet I. Meek for her commitment to the promotion of researchby her continuousencouragement of such efforts and for providing financial support from the Lima campusof The Ohio StateUniversity. We havereceivedimmensecooperationfrom all the refereeswho, meticulouslyand in a very short time, provided us with their reports in spite of their busy schedules. We expressour sincerethanks to all of them. Finally, we thank Ms. Cindy White for her excellent job in typing parts of this volume. We are pleasedto dedicatethis volume to ProfessorBruno J. Miiller on the occasionof his retirementfor his many contributionsto the Theory of Rings and Modules. As this volume was going to presswe have learned that ProfessorCarl Faith is retiring this year.

Fascinated by the diversity of living organisms, humans have always been curious about its origin. Darwin was the first to provide the scholary and persuasive thesis for gradual evolution and speciation under natural selection. Although we now have much information on evolution, we still don't understand it in detail. Many questions still remain open due to the complexity and multiplicity of interacting factors. Several approaches mainly arising from population ecology and genetics are presented in this book in order to help understand genetic variation and evolution.

This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.

Rye first appeared rather late in the history of human civilization. The oldest archaeological records of rye date from the Hallstatt period in Silesia, Thuringia and Westfalia and from the Lacene period. After the pioneering work of N. 1. V AVILOV on the origin of cultivated plants three broad classes came in recognition: wild, weedy and cultivated rye. As a crop, rye is most winterhardy of all cereals so that in Northern Europe its cultivation reaches beyond the Arctic circle in Finland. While Soviet Russia contributes most to the total world production, in Finland, Poland, Germany, Sweden, Netherlands and Belgium also its rank is high among grain crops. It is striking to note that for the past many years, research on practical agronomical and breeding problems has been quite active in these countries and current ly attempts to improve rye are being made on modern lines. Some of the main problems in this field concern with the development of hybrid varieties, improvement of autotetraploid fertility, use of best pollina tion procedures to obtain highly self-fertile lines and the transfer of rye characters to wheat as such or in the form of amphiploid Triticales. In Russia, however, the Michurinist agrobiologists are primarily engaged in the study of interspecific conversions, branched ear types and nutritional methods of improving varieties, and perhaps this is one reason of only little having been known about rye genetics.

or fruit production as a consequence of the lack of optimum pollination conditions (CLARK and FRYER, 1920; ARMSTRONG and WHITE, 1935; VALLEAU, 1918; KVAALE, 1927; and many others). In order to mini mize the influence of poor pollen producers, systematic planning of a field planting or an orchard might be necessary. Above all, the im portant reason for its wide popularity is its potential use in the com mercial production of hybrid seed. A male-sterile plant is an effective female for a crossing program and its employment renders the labori ous procedure of emasculation superfluous. ]ONES and EMSWELLER (1937) and STEPHENS (1937) were probably the first to outline a scheme of its application in onion and sorghum respectively. However certain specific problems have limited the practicability and hence some of them will be mentioned in a later seetion (Section VIII). Lately several attempts have been made to obtain some chemie al method for the artificial induction of male sterility. However, for a successful approach to the induction problem a thorough understan ding of various pathways that bring about pollen abortion in naturally occurring cases, would be of great value. It may be hoped that data from these induction experiments alongwith the available biochemi cal analyses would lead to the emergence and elucidation of useful information of both theoretical and practical interest.

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules.

This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.

This book discusses the revolution of cycles and rhythms that is expected to take place in different branches of science and engineering in the 21st century, with a focus on communication and information processing. It presents high-quality papers in vibration sciences, rhythms and oscillations, neurosciences, mathematical sciences, and communication. It includes major topics in engineering and structural mechanics, computer sciences, biophysics and biomathematics, as well as other related fields. Offering valuable insights, it also inspires researchers to work in these fields. The papers included in this book were presented at the 1st International Conference on Engineering Vibration, Communication and Information Processing (ICoEVCI-2018), India.