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Rings Related To Stable Range Conditions


Rings Related To Stable Range Conditions
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Rings Related To Stable Range Conditions


Rings Related To Stable Range Conditions
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Author : Huanyin Chen
language : en
Publisher: World Scientific
Release Date : 2011

Rings Related To Stable Range Conditions written by Huanyin Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.


This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.



Exercises In Classical Ring Theory


Exercises In Classical Ring Theory
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Exercises In Classical Ring Theory written by T.Y. Lam 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 2013-06-29 with Mathematics categories.


Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.



The Classical Groups And K Theory


The Classical Groups And K Theory
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Author : Alexander J. Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

The Classical Groups And K Theory written by Alexander J. Hahn 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 2013-03-09 with Mathematics categories.


It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).



Recent Research On Pure And Applied Algebra


Recent Research On Pure And Applied Algebra
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Author : Omar Pordavi
language : en
Publisher: Nova Publishers
Release Date : 2003

Recent Research On Pure And Applied Algebra written by Omar Pordavi and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


This volume gathers results in pure and applied algebra from researchers around the globe. The selection of these papers was carried out under the auspices of a special editorial board.



Ring Theory And Its Applications


Ring Theory And Its Applications
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Author : Dinh Van Huynh
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-02-21

Ring Theory And Its Applications written by Dinh Van Huynh 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 2014-02-21 with Mathematics categories.


This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.



Rings Close To Regular


Rings Close To Regular
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Author : A.A. Tuganbaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Rings Close To Regular written by A.A. Tuganbaev 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 2013-03-09 with Mathematics categories.


Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular.



Proceedings Of The Conference On Orders Group Rings And Related Topics


Proceedings Of The Conference On Orders Group Rings And Related Topics
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Author : J. S. Hsia
language : en
Publisher: Springer
Release Date : 2006-11-15

Proceedings Of The Conference On Orders Group Rings And Related Topics written by J. S. Hsia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.




Introduction To Linear Control Systems


Introduction To Linear Control Systems
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Author : Yazdan Bavafa-Toosi
language : en
Publisher: Academic Press
Release Date : 2017-09-19

Introduction To Linear Control Systems written by Yazdan Bavafa-Toosi and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Technology & Engineering categories.


Introduction to Linear Control Systems is designed as a standard introduction to linear control systems for all those who one way or another deal with control systems. It can be used as a comprehensive up-to-date textbook for a one-semester 3-credit undergraduate course on linear control systems as the first course on this topic at university. This includes the faculties of electrical engineering, mechanical engineering, aerospace engineering, chemical and petroleum engineering, industrial engineering, civil engineering, bio-engineering, economics, mathematics, physics, management and social sciences, etc. The book covers foundations of linear control systems, their raison detre, different types, modelling, representations, computations, stability concepts, tools for time-domain and frequency-domain analysis and synthesis, and fundamental limitations, with an emphasis on frequency-domain methods. Every chapter includes a part on further readings where more advanced topics and pertinent references are introduced for further studies. The presentation is theoretically firm, contemporary, and self-contained. Appendices cover Laplace transform and differential equations, dynamics, MATLAB and SIMULINK, treatise on stability concepts and tools, treatise on Routh-Hurwitz method, random optimization techniques as well as convex and non-convex problems, and sample midterm and endterm exams. The book is divided to the sequel 3 parts plus appendices. PART I: In this part of the book, chapters 1-5, we present foundations of linear control systems. This includes: the introduction to control systems, their raison detre, their different types, modelling of control systems, different methods for their representation and fundamental computations, basic stability concepts and tools for both analysis and design, basic time domain analysis and design details, and the root locus as a stability analysis and synthesis tool. PART II: In this part of the book, Chapters 6-9, we present what is generally referred to as the frequency domain methods. This refers to the experiment of applying a sinusoidal input to the system and studying its output. There are basically three different methods for representation and studying of the data of the aforementioned frequency response experiment: these are the Nyquist plot, the Bode diagram, and the Krohn-Manger-Nichols chart. We study these methods in details. We learn that the output is also a sinusoid with the same frequency but generally with different phase and magnitude. By dividing the output by the input we obtain the so-called sinusoidal or frequency transfer function of the system which is the same as the transfer function when the Laplace variable s is substituted with . Finally we use the Bode diagram for the design process. PART III: In this part, Chapter 10, we introduce some miscellaneous advanced topics under the theme fundamental limitations which should be included in this undergraduate course at least in an introductory level. We make bridges between some seemingly disparate aspects of a control system and theoretically complement the previously studied subjects. Appendices: The book contains seven appendices. Appendix A is on the Laplace transform and differential equations. Appendix B is an introduction to dynamics. Appendix C is an introduction to MATLAB, including SIMULINK. Appendix D is a survey on stability concepts and tools. A glossary and road map of the available stability concepts and tests is provided which is missing even in the research literature. Appendix E is a survey on the Routh-Hurwitz method, also missing in the literature. Appendix F is an introduction to random optimization techniques and convex and non-convex problems. Finally, appendix G presents sample midterm and endterm exams, which are class-tested several times.



Rings Modules And Codes


Rings Modules And Codes
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Author : André Leroy
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-12

Rings Modules And Codes written by André Leroy 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 2019-04-12 with Mathematics categories.


This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.



Advances In Algebra


Advances In Algebra
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Author : K. P. Shum
language : en
Publisher: World Scientific
Release Date : 2003

Advances In Algebra written by K. P. Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


This is the proceedings of the ICM2002 Satellite Conference on Algebras. Over 175 participants attended the meeting. The opening ceremony included an address by R. Gonchidorsh, former vice-president of the Mongolian Republic in Uaalannbaatar. The topics covered at the conference included general algebras, semigroups, groups, rings, hopf algebras, modules, codes, languages, automation theory, graphs, fuzz algebras and applications.