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Occasioned by the international conference "Rings and
Factorizations" held in February 2018 at University of Graz,
Austria, this volume represents a wide range of research trends in
the theory of commutative and non-commutative rings and their
modules, including multiplicative ideal theory, Dedekind and Krull
rings and their generalizations, rings of integer
valued-polynomials, topological aspects of ring theory,
factorization theory in rings and semigroups and direct-sum
decompositions of modules. The volume will be of interest to
researchers seeking to extend or utilize work in these areas as
well as graduate students wishing to find entryways into active
areas of current research in algebra. A novel aspect of the volume
is an emphasis on how diverse types of algebraic structures and
contexts (rings, modules, semigroups, categories) may be treated
with overlapping and reinforcing approaches.
Occasioned by the international conference "Rings and
Factorizations" held in February 2018 at University of Graz,
Austria, this volume represents a wide range of research trends in
the theory of commutative and non-commutative rings and their
modules, including multiplicative ideal theory, Dedekind and Krull
rings and their generalizations, rings of integer
valued-polynomials, topological aspects of ring theory,
factorization theory in rings and semigroups and direct-sum
decompositions of modules. The volume will be of interest to
researchers seeking to extend or utilize work in these areas as
well as graduate students wishing to find entryways into active
areas of current research in algebra. A novel aspect of the volume
is an emphasis on how diverse types of algebraic structures and
contexts (rings, modules, semigroups, categories) may be treated
with overlapping and reinforcing approaches.
This book consists of both expository and research articles
solicited from speakers at the conference entitled "Arithmetic and
Ideal Theory of Rings and Semigroups," held September 22-26, 2014
at the University of Graz, Graz, Austria. It reflects recent trends
in multiplicative ideal theory and factorization theory, and brings
together for the first time in one volume both commutative and
non-commutative perspectives on these areas, which have their roots
in number theory, commutative algebra, and algebraic geometry.
Topics discussed include topological aspects in ring theory, Prufer
domains of integer-valued polynomials and their monadic submonoids,
and semigroup algebras. It will be of interest to practitioners of
mathematics and computer science, and researchers in multiplicative
ideal theory, factorization theory, number theory, and algebraic
geometry.
This book consists of both expository and research articles
solicited from speakers at the conference entitled "Arithmetic and
Ideal Theory of Rings and Semigroups," held September 22-26, 2014
at the University of Graz, Graz, Austria. It reflects recent trends
in multiplicative ideal theory and factorization theory, and brings
together for the first time in one volume both commutative and
non-commutative perspectives on these areas, which have their roots
in number theory, commutative algebra, and algebraic geometry.
Topics discussed include topological aspects in ring theory, Prufer
domains of integer-valued polynomials and their monadic submonoids,
and semigroup algebras. It will be of interest to practitioners of
mathematics and computer science, and researchers in multiplicative
ideal theory, factorization theory, number theory, and algebraic
geometry.
Commutative algebra is a rapidly growing subject that is developing
in many different directions. This volume presents several of the
most recent results from various areas related to both Noetherian
and non-Noetherian commutative algebra. This volume contains a
collection of invited survey articles by some of the leading
experts in the field. The authors of these chapters have been
carefully selected for their important contributions to an area of
commutative-algebraic research. Some topics presented in the volume
include: generalizations of cyclic modules, zero divisor graphs,
class semigroups, forcing algebras, syzygy bundles, tight closure,
Gorenstein dimensions, tensor products of algebras over fields, as
well as many others. This book is intended for researchers and
graduate students interested in studying the many topics related to
commutative algebra.
This volume, a tribute to the work of Robert Gilmer, consists of
twenty-four articles authored by his most prominent students and
followers. These articles combine surveys of past work by Gilmer
and others, recent results which have never before seen print, open
problems, and extensive bibliographies. The entire collection
provides an in-depth overview of the topics of research in a
significant and large area of commutative algebra.
Commutative algebra is a rapidly growing subject that is developing
in many different directions. This volume presents several of the
most recent results from various areas related to both Noetherian
and non-Noetherian commutative algebra. This volume contains a
collection of invited survey articles by some of the leading
experts in the field. The authors of these chapters have been
carefully selected for their important contributions to an area of
commutative-algebraic research. Some topics presented in the volume
include: generalizations of cyclic modules, zero divisor graphs,
class semigroups, forcing algebras, syzygy bundles, tight closure,
Gorenstein dimensions, tensor products of algebras over fields, as
well as many others. This book is intended for researchers and
graduate students interested in studying the many topics related to
commutative algebra.
This volume contains selected refereed papers based on lectures
presented at the a ~Fifth International Fez Conference on
Commutative Algebra and Applicationsa (TM) that was held in Fez,
Morocco in June 2008. The volume represents new trends and areas of
classical research within the field, with contributions from many
different countries. In addition, the volume has as a special focus
the research and influence of Alain Bouvier on commutative algebra
over the past thirty years.
For over forty years, Robert Gilmer's numerous articles and books
have had a tremendous impact on research in commutative algebra. It
is not an exaggeration to say that most articles published today in
non-Noetherian ring theory, and some in Noetherian ring theory as
well, originated in a topic that Gilmer either initiated or
enriched by his work. This volume, a tribute to his work, consists
of twenty-four articles authored by Robert Gilmer's most prominent
students and followers. These articles combine surveys of past work
by Gilmer and others, recent results which have never before seen
print, open problems, and extensive bibliographies. In a concluding
article, Robert Gilmer points out directions for future research,
highlighting the open problems in the areas he considers of
importance. Robert Gilmer's article is followed by the complete
list of his published works, his mathematical genealogical tree,
information on the writing of his four books, and reminiscences
about Robert Gilmer's contributions to the stimulating research
environment in commutative algebra at Florida State in the middle
1960s. in a significant and large area of commutative algebra.
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