Graded and Filtered Rings and Modules, C. Nastasescu; F. van Oystaeyen

Автор: Marco Fontana; Sophie Frisch; Sarah Glaz; Francesc
Название: Rings, Polynomials, and Modules
ISBN: 3319658727 ISBN-13(EAN): 9783319658728
Издательство: Springer
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Описание:

Preface.- 1 Reducing Fractions to Lowest Terms.- 2 Unique Factorization in Torsion-free Modules.- 3 n-Absorbing Ideals of Commutative Rings and Recent Progresses on Three Conjectures: A Survey.- 4 Embedding Dimension and Codimension of Tensor Products of Algebras Over a Field.- 5 Minimal Generating Sets for the D-Algebra Int(S, D).- 6 Algebraic Entropy in Locally Linearly Compact Vector Spaces.- 7 Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat.- 8 Commutative Rings with a Prescribed Number of Isomorphism Classes of Minimal Ring Extensions.- 9 Applications of Multisymmetric Syzygies in Invariant Theory.- 10 Functorial Properties of Star Operations: New Developments.- 11 Systems of Sets of Lengths: Transfer Krull Monoids Versus Weakly Krull Monoids.- 12 Corner's Realization Theorems from the Viewpoint of Algebraic Entropy.- 13 Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks.- 14 Divisorial Prime Ideals in Prьfer Domains.- 15 A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative.- 16 Quasi-Prьfer Extensions of Rings.- 17 A Note on Analytically Irreducible Domains.- 18 Integer-valued Polynomials on Algebras: A Survey of Recent Results and Open Questions.

Автор: Birkenmeier Gary F., Park Jae Keol, Rizvi S. Tariq
Название: Extensions of Rings and Modules
ISBN: 0387927158 ISBN-13(EAN): 9780387927152
Издательство: Springer
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Описание: This book explores in detail the "extensions" of rings and modules. It covers mathematical interdiscipllinary applications throughout and features exercises and open problems.

Автор: Stuart A. Steinberg
Название: Lattice-ordered Rings and Modules
ISBN: 1489982973 ISBN-13(EAN): 9781489982971
Издательство: Springer
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Описание: This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included. Key topics include: lattice-ordered groups, rings, and fields; Archimedean $l$-groups; f-rings and larger varieties of $l$-rings; the category of f-modules; various commutativity results. This text may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules.