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Author: Daniel Anderson
Publisher: Routledge
ISBN: 1351448943
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
Author: Daniel Anderson
Publisher: Routledge
ISBN: 1351448943
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
Author: Ayman Badawi
Publisher: Springer
ISBN: 9811370281
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This book highlights the contributions of the eminent mathematician and leading algebraist David F. Anderson in wide-ranging areas of commutative algebra. It provides a balance of topics for experts and non-experts, with a mix of survey papers to offer a synopsis of developments across a range of areas of commutative algebra and outlining Anderson’s work. The book is divided into two sections—surveys and recent research developments—with each section presenting material from all the major areas in commutative algebra. The book is of interest to graduate students and experienced researchers alike.
Author: Scott T. Chapman
Publisher: CRC Press
ISBN: 1420028243
Category : Mathematics
Languages : en
Pages : 410
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Book Description
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
Author: Ayman Badawi
Publisher: Nova Publishers
ISBN: 9781590339268
Category : Computers
Languages : en
Pages : 228
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Book Description
Trends in Commutative Rings Research
Author: Paul-Jean Cahen
Publisher: CRC Press
ISBN: 1000946762
Category : Mathematics
Languages : en
Pages : 489
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Book Description
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: David J. Grynkiewicz
Publisher: Springer Nature
ISBN: 303114869X
Category : Mathematics
Languages : en
Pages : 291
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Book Description
This book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory’s Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra) This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.
Author: S.T. Chapman
Publisher: Springer Science & Business Media
ISBN: 1475731809
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Commutative Ring Theory emerged as a distinct field of research in math ematics only at the beginning of the twentieth century. It is rooted in nine teenth century major works in Number Theory and Algebraic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of activity in this area, including: a large number of conferences and special sections at national and international meetings dedicated to presenting its results, an abundance of articles in scientific journals, and a substantial number of books capturing some of its topics. This rapid growth, and the occasion of the new Millennium, prompted us to embark on a project aimed at presenting an overview of the recent research in the area. With this in mind, we invited many of the most prominent researchers in Non-Noetherian Commutative Ring Theory to write expository articles representing the most recent topics of research in this area.
Author: Alfred Geroldinger
Publisher: CRC Press
ISBN: 1420003208
Category : Mathematics
Languages : en
Pages : 723
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Book Description
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza
Author: Ayman Badawi
Publisher: Nova Biomedical Books
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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Book Description
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:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 796
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Book Description
