Integer Valued Polynomials Over Quaternion Rings
DOWNLOAD
Download Integer Valued Polynomials Over Quaternion Rings PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Integer Valued Polynomials Over Quaternion Rings book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Integer Valued Polynomials Over Quaternion Rings
DOWNLOAD
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.
Rings Polynomials And Modules
DOWNLOAD
Author : Marco Fontana
language : en
Publisher: Springer
Release Date : 2017-11-11
Rings Polynomials And Modules written by Marco Fontana and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-11 with Mathematics categories.
This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.
Commutative Algebra
DOWNLOAD
Author : Marco Fontana
language : en
Publisher: Springer
Release Date : 2014-07-15
Commutative Algebra written by Marco Fontana and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-15 with Mathematics categories.
This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
Current Problems Of Applied Mathematics And Computer Systems
DOWNLOAD
Author : Anatoly Alikhanov
language : en
Publisher: Springer Nature
Release Date : 2024-09-01
Current Problems Of Applied Mathematics And Computer Systems written by Anatoly Alikhanov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-01 with Technology & Engineering categories.
This book is based on the best papers accepted for presentation during the International Conference on Current Problems of Applied Mathematics and Computer Systems (APAMCS-2023). The book includes research materials on mathematical problems and solutions in the field of scientific computing, artificial intelligence, data analysis and modular computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in data analysis and modular computing include contributions in the field of deep learning, neural networks, mathematical statistics, machine learning methods, residue number system and artificial intelligence. In addition, some articles focus on mathematical modeling of nonlinear physical phenomena. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of scientific computing, parallel computing, computer technology, machine learning, information security and mathematical education
Quaternion Algebras
DOWNLOAD
Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28
Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Integer Valued Polynomials
DOWNLOAD
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.
New Frontiers In Number Theory And Applications
DOWNLOAD
Author : Jordi Guàrdia
language : en
Publisher: Springer Nature
Release Date : 2024-05-27
New Frontiers In Number Theory And Applications written by Jordi Guàrdia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-27 with Mathematics categories.
This contributed volume presents recent advances as well as new directions in number theory and its applications. Algebraic and analytic number theory are the main focus with chapters showing how these areas are rapidly evolving. By gathering authors from over seven countries, readers will gain an international perspective on the current state of research as well as potential avenues to explore. Specific topics covered include: Algebraic Number Theory Elliptic curves and Cryptography Hopf Galois theory Analytic and elementary number theory and applications New Frontiers in Number Theory and Applications will appeal to researchers interested in gaining a global view of current research in number theory.
Undergraduate Algebra
DOWNLOAD
Author : Matej Brešar
language : en
Publisher: Springer
Release Date : 2019-05-15
Undergraduate Algebra written by Matej Brešar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-15 with Mathematics categories.
This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory. Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.
Notices Of The American Mathematical Society
DOWNLOAD
Author : American Mathematical Society
language : en
Publisher:
Release Date : 1974
Notices Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Electronic journals categories.
Contains articles of significant interest to mathematicians, including reports on current mathematical research.
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques
DOWNLOAD
Author : Ashish Goel
language : en
Publisher: Springer
Release Date : 2008-08-28
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques written by Ashish Goel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-28 with Computers categories.
This volume contains the papers presented at the 11th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2008) and the 12th International Workshop on Randomization and Computation (RANDOM 2008), which took place concurrently at the MIT (M- sachusetts Institute of Technology) in Boston, USA, during August 25–27, 2008. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 11th in the series after Aalborg (1998), Berkeley (1999), Saarbru ̈cken (2000), Berkeley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 12th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), and Princeton (2007). Topics of interest for APPROX and RANDOM are: design and analysis of - proximation algorithms, hardness of approximation, small space, sub-linear time, streaming, algorithms, embeddings and metric space methods, mathematical programming methods, combinatorial problems in graphs and networks, game t- ory, markets, economic applications, geometric problems, packing, covering, scheduling, approximate learning, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and - beddings, error-correcting codes, average-case analysis, property testing, com- tational learning theory, and other applications of approximation and randomness.