Integer Valued Polynomials
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Integer Valued Polynomials
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Author : Paul-Jean Cahen
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Integer Valued Polynomials written by Paul-Jean Cahen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. Polya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain $D$ and the polynomials (with coefficients in its quotient field) mapping $D$ into itself. They form a $D$-algebra - that is, a $D$-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a rich structure, and the very numerous questions it raises allow a thorough exploration of commutative algebra. Here is the first book devoted entirely to this topic. This book features: thorough reviews of many published works; self-contained text with complete proofs; and numerous exercises.
Integer Valued Polynomials Over Quaternion Rings
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Author : Nicholas J. Werner
language : en
Publisher:
Release Date : 2010
Integer Valued Polynomials Over Quaternion Rings written by Nicholas J. Werner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Abstract: When D is an integral domain with field of fractions K, the ring Int(D) of integer-valued polynomials over D is defined to be the set of all polynomials f(a) in K[x] such that f(a) is in D for all a in D. The goal of this dissertation is to extend the integer-valued polynomial construction to certain noncommutative rings. Specifically, for any ring R, we define the R-algebra RQ to be the set of elements of the form a + bi + cj + dk, where i, j, and k are the standard quaternion units satisfying the relations i^2 = j^2 = -1 and ij = k = -ji. When this is done with the integers Z, we obtain a noncommutative ring ZQ; when this is done with the rational numbers Q, we get a division ring QQ. Our main focus is on the construction and study of Int(ZQ), the set of integer-valued polynomials over ZQ. We also consider Int(R), where R is an overring of ZQ in QQ. In this treatise, we prove that for such an R, Int(R) has a ring structure and investigate elements, generating sets, and prime ideals of Int(R). The final chapter examines the idea of integer-valued polynomials on subsets of ZQ.
Polynomials That Are Integer Valued On The Fibonacci Numbers
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Author : Kira Scheibelhut
language : en
Publisher:
Release Date : 2013
Polynomials That Are Integer Valued On The Fibonacci Numbers written by Kira Scheibelhut and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Integer Valued Polynomials
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Author : Sanjai K. Gupta
language : en
Publisher:
Release Date : 1999
Integer Valued Polynomials written by Sanjai K. Gupta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Polynomials
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Author : Victor V. Prasolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-23
Polynomials written by Victor V. Prasolov 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 2009-09-23 with Mathematics categories.
From the reviews: "... Despite the appearance [...] in a series titled Algorithms and Computation of Mathematics, computation occupies only a small part of the monograph. It is best described as a useful reference for one's personal collection and a text for a full-year course given to graduate or even senior undergraduate students. [...] the book under review is worth purchasing for the library and possibly even for one's own collection. The author's interest in the history and development of this area is evident, and we have pleasant glimpses of progress over the last three centuries [...] the reader gains a synopsis of and guide to the literature ..." E.Barbeau, SIAM Review 47:3, 2005. "This is an exposition of polynomial theory and results, both classical and modern. [...] the volume is packed with results and proofs that are well organised thematically [...] What is unusual is to have a text that embraces and intermingles both analytic and algebraic aspects of the theory..." S.D.Cohen, Math.Reviews 2005
Commutative Algebra And Its Applications
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Author : Marco Fontana
language : en
Publisher: Walter de Gruyter
Release Date : 2009-09-04
Commutative Algebra And Its Applications written by Marco Fontana and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-04 with Mathematics categories.
This volume contains selected refereed papers based on lectures presented at the ‘Fifth International Fez Conference on Commutative Algebra and Applications’ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Essays On Numbers And Figures
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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Essays On Numbers And Figures written by Viktor Vasilʹevich Prasolov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The English translation of a book originally published in Russian. It contains 20 essays, each dealing with a separate mathematical topic. The topics range from brilliant mathematical statements with interesting proofs, to simple and effective methods of problem-solving, to interesting properties of polynomials, to exceptional points of the triangle. Many of the topics have a long and interesting history and the author has lectured on them to students worldwide. The essays are independent of one another for the most part, and each presents a vivid mathematical result that led to current research in number theory, geometry, polynomial algebra, or topology.
The Integer Valued Polynomials On Lucas Numbers
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Author : Amitabh Kumer Halder
language : en
Publisher:
Release Date : 2017
The Integer Valued Polynomials On Lucas Numbers written by Amitabh Kumer Halder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
An integer-valued polynomial on a subset, S, of the set of integers, Z, is a polynomial f(x) 2 Q[x] such that f(S) Z. The collection, Int(S;Z), of such integer-valued polynomials forms a ring with many interesting properties. The concept of p-ordering and the associated p-sequence due to Bhargava [2] is used for nding integer-valued polynomials on any subset, S, of Z. In this thesis, we concentrate on extending the work of Keith Johnson and Kira Scheibelhut [14] for the case S = L, the Lucas numbers, where they work on integervalued polynomials on S = F, Fibonacci numbers. We also study integer-valued polynomials on the general 3 term recursion sequence, G, of integers for a given pair of initial values with some interesting properties. The results are well-agreed with those of [14].
Multiplicative Ideal Theory And Factorization Theory
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Author : Scott Chapman
language : en
Publisher: Springer
Release Date : 2016-07-29
Multiplicative Ideal Theory And Factorization Theory written by Scott Chapman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-29 with Mathematics categories.
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
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."