Arithmetical Properties Of Commutative Rings And Monoids
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Arithmetical Properties of Commutative Rings and Monoids
The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the w
Ideal Theory of Commutative Rings and Monoids
This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.
Arithmetical Rings and Endomorphisms
Author: Askar Tuganbaev
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2019-06-04
This book offers a comprehensive account of not necessarily commutative arithmetical rings, examining structural and homological properties of modules over arithmetical rings and summarising the interplay between arithmetical rings and other rings, whereas modules with extension properties of submodule endomorphisms are also studied in detail. Graduate students and researchers in ring and module theory will find this book particularly valuable.