Some Types Of Unique Factorization In Integral Domains
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Some Types Of Unique Factorization In Integral Domains
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Author :
language : en
Publisher:
Release Date : 1968
Some Types Of Unique Factorization In Integral Domains written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Factorization In Integral Domains
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Author : Daniel Anderson
language : en
Publisher: Routledge
Release Date : 2017-11-13
Factorization In Integral Domains written by Daniel Anderson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-13 with Mathematics categories.
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.
Advances In Commutative Ring Theory
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Author : David Dobbs
language : en
Publisher: CRC Press
Release Date : 2023-08-25
Advances In Commutative Ring Theory written by David Dobbs and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-25 with Mathematics categories.
"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."
Factoring Ideals In Integral Domains
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Author : Marco Fontana
language : en
Publisher: Springer Science & Business Media
Release Date : 2013
Factoring Ideals In Integral Domains written by Marco Fontana and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.
Learning Abstract Algebra With Isetl
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Author : Ed Dubinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture.
Abstract Algebra
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Author : Jonathan K. Hodge
language : en
Publisher: CRC Press
Release Date : 2023-12-19
Abstract Algebra written by Jonathan K. Hodge and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-19 with Mathematics categories.
Abstract Algebra: An Inquiry-Based Approach, Second Edition not only teaches abstract algebra, but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The second edition of this unique, flexible approach builds on the success of the first edition. The authors offer an emphasis on active learning, helping students learn algebra by gradually building both their intuition and their ability to write coherent proofs in context. The goals for this text include: Allowing the flexibility to begin the course with either groups or rings. Introducing the ideas behind definitions and theorems to help students develop intuition. Helping students understand how mathematics is done. Students will experiment through examples, make conjectures, and then refine or prove their conjectures. Assisting students in developing their abilities to effectively communicate mathematical ideas. Actively involving students in realizing each of these goals through in-class and out-of-class activities, common in-class intellectual experiences, and challenging problem sets. Changes in the Second Edition Streamlining of introductory material with a quicker transition to the material on rings and groups. New investigations on extensions of fields and Galois theory. New exercises added and some sections reworked for clarity. More online Special Topics investigations and additional Appendices, including new appendices on other methods of proof and complex roots of unity. Encouraging students to do mathematics and be more than passive learners, this text shows students the way mathematics is developed is often different than how it is presented; definitions, theorems, and proofs do not simply appear fully formed; mathematical ideas are highly interconnected; and in abstract algebra, there is a considerable amount of intuition to be found.
Basic Algebra
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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28
Basic Algebra written by Anthony W. Knapp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-28 with Mathematics categories.
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Multiplicative Ideal Theory In Commutative Algebra
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Author : James W. Brewer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-15
Multiplicative Ideal Theory In Commutative Algebra written by James W. Brewer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-15 with Mathematics categories.
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. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.
Abstract Analytic Number Theory
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Author : Knopfmacher
language : en
Publisher: Newnes
Release Date : 2009-02-04
Abstract Analytic Number Theory written by Knopfmacher and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-04 with Technology & Engineering categories.
North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.
The Nature And Growth Of Modern Mathematics
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Author : Edna Ernestine Kramer
language : en
Publisher: Princeton University Press
Release Date : 1982
The Nature And Growth Of Modern Mathematics written by Edna Ernestine Kramer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.