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Author : Ayman Badawi
Publisher : Nova Publishers
Page : 228 pages
File Size : 43,7 Mb
Release : 2004
Category : Computers
ISBN : 1590339266
Trends in Commutative Rings Research
Author : Ayman Badawi
Publisher : Nova Publishers
Page : 220 pages
File Size : 44,5 Mb
Release : 2006
Category : Mathematics
ISBN : 1600210651
Focus on Commutative Rings Research
Author : Christopher Francisco,Lee C. Klingler,Sean M. Sather-Wagstaff,Janet C. Vassilev
Publisher : Walter de Gruyter
Page : 329 pages
File Size : 49,6 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9783110278606
This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.
Author : David Dobbs
Publisher : CRC Press
Page : 578 pages
File Size : 42,6 Mb
Release : 2023-08-25
Category : Mathematics
ISBN : 9781000939637
"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
Author : Paul-Jean Cahen
Publisher : Unknown
Page : 0 pages
File Size : 48,6 Mb
Release : 1997
Category : MATHEMATICS
ISBN : 1000951723
Presenting the proceedings of the recently held Second International Conference on Commutative Ring Theory in Fes, Morocco, this up-to-date reference details the latest developments in commutative algebra - highlighting the theory of rings and ideals. Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers spectra of rings ... dimension theory ... chain conditions ... class groups ... duals of ideals ... Mori and Krull domains ... Prufer domains ... integer-valued polynomials ... semigroup rings ... seminormalization and weak normalization ... generators of ideals ... homological aspects ... and more. Furnishing over 580 literature citations, allowing further in-depth study of particular topics, Commutative Ring Theory is a vital resource for research mathematicians, algebraists, commutative ring theorists, and graduate students in these disciplines.
Author : Askar A. Tuganbaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 175 pages
File Size : 46,9 Mb
Release : 2019-06-04
Category : Mathematics
ISBN : 9783110659825
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.
Author : A. R. Tyler
Publisher : Nova Publishers
Page : 252 pages
File Size : 54,6 Mb
Release : 2007
Category : Computers
ISBN : 1600216889
An expert system, also known as a knowledge based system, is a computer program that contains some of the subject-specific knowledge of one or more human experts. This class of program was first developed by researchers in artificial intelligence during the 1960s and 1970s and applied commercially throughout the 1980s. The most common form of expert systems is a program made up of a set of rules that analyse information usually supplied by the user of the system) about a specific class of problems, as well as providing mathematical analysis of the problem(s), and, depending upon their design, recommend a course of user action in order to implement corrections. It is a system that utilises what appear to be reasoning capabilities to reach conclusions. This book presents important research on in this dynamic field.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,6 Mb
Release : 1982
Category : Electronic
ISBN : OCLC:434502753
Author : Scott T. Chapman
Publisher : CRC Press
Page : 128 pages
File Size : 47,7 Mb
Release : 2017-08-09
Category : Electronic
ISBN : 1138402079
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 world to review recent major results. The first seven chapters demonstrate the diversity of approaches taken in studying nonunique factorizations and serve both as an introduction to factorization theory and as a survey of current trends and results. The remaining chapters reflect research motivated by arithmetical properties of commutative rings and monoids.
Author : Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 47,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9783110250404
This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.
Author : Ayman Badawi,Mohammad Reza Vedadi,Siamak Yassemi,Ahmad Yousefian Darani
Publisher : Springer
Page : 149 pages
File Size : 54,7 Mb
Release : 2018-03-01
Category : Mathematics
ISBN : 9783319741956
Based on the 4th Seminar on Algebra and its Applications organized by the University of Mohaghegh Ardabili, this volume highlights recent developments and trends in algebra and its applications. Selected and peer reviewed, the contributions in this volume cover areas that have flourished in the last few decades, including homological algebra, combinatorial algebra, module theory and linear algebra over rings, multiplicative ideal theory, and integer-valued polynomials. Held biennially since 2010, SAA introduces Iranian faculty and graduate students to important ideas in the mainstream of algebra and opens channels of communication between Iranian mathematicians and algebraists from around the globe to facilitate collaborative research. Ideal for graduate students and researchers in the field, these proceedings present the best of the seminar’s research achievements and new contributions to the field.
Author : Ayman Badawi
Publisher : Nova Biomedical Books
Page : 232 pages
File Size : 47,6 Mb
Release : 2002
Category : Mathematics
ISBN : PSU:000048767293
This volume presents up-to-date references on the latest developments in commutative algebra and related areas featuring 19 original articles on fundamental topics of current interest. It covers arithmetical rings, pullback construction, elasticity and factorisation, A + XB(X) domains, distinguished domains, going-down domains, semistar operations, star-operations, trace properties, pseudo-valuation rings, modules, zerodivisor graphs, normal maximal ideals and numerical semi-groups. This is a vital resource for research mathematicians, algebraists, commutative ring theorists and graduate students in these disciplines.
Author : Toma Albu,Gary F. Birkenmeier,Ali Erdogan,Adnan Tercan
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 48,9 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783034600071
This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
Author : Paul-Jean Cahen,Marco Fontana,Evan Houston,Salah-Eddine Kabbaj
Publisher : CRC Press
Page : 489 pages
File Size : 51,7 Mb
Release : 2023-06-14
Category : Mathematics
ISBN : 9781000946765
Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.
Author : Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer Nature
Page : 341 pages
File Size : 41,5 Mb
Release : 2020-06-02
Category : Mathematics
ISBN : 9783030434168
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.
