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Author : Simeon Ivanov
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 50,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821831402
This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.
Author : Grégory Berhuy
Publisher : Cambridge University Press
Page : 328 pages
File Size : 50,9 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9781139490887
This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.
Author : Stephen Urban Chase,D. K. Harrison,Alex Rosenberg
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 42,5 Mb
Release : 1969
Category : Commutative rings
ISBN : 9780821812525
Author : Victor P Snaith
Publisher : World Scientific Publishing Company
Page : 228 pages
File Size : 52,9 Mb
Release : 2003-09-29
Category : Mathematics
ISBN : 9789813102231
This book is ideally suited for a two-term undergraduate algebra course culminating in a discussion on Galois theory. It provides an introduction to group theory and ring theory en route. In addition, there is a chapter on groups — including applications to error-correcting codes and to solving Rubik's cube. The concise style of the book will facilitate student-instructor discussion, as will the selection of exercises with various levels of difficulty. For the second edition, two chapters on modules over principal ideal domains and Dedekind domains have been added, which are suitable for an advanced undergraduate reading course or a first-year graduate course.
Author : Celine Carstensen,Benjamin Fine,Gerhard Rosenberger
Publisher : Walter de Gruyter
Page : 381 pages
File Size : 41,5 Mb
Release : 2011
Category : Language Arts & Disciplines
ISBN : 9783110250084
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics.
Author : V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 50,7 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9780821872888
Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.
Author : Teresa Crespo,Zbigniew Hajto
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 54,7 Mb
Release : 2011
Category : Computers
ISBN : 9780821853184
Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory. This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book. This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields.
Author : Andy R. Magid
Publisher : CRC Press
Page : 262 pages
File Size : 42,6 Mb
Release : 2020-09-10
Category : Mathematics
ISBN : 9781000116816
"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."
Author : Mohamed Ayad
Publisher : World Scientific Publishing Company
Page : 452 pages
File Size : 54,8 Mb
Release : 2018-04-26
Category : Mathematics
ISBN : 9789813238329
Author : Siegfried Bosch
Publisher : Springer
Page : 352 pages
File Size : 53,5 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783319951775
The material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date.
Author : Celine Carstensen-Opitz,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 421 pages
File Size : 49,7 Mb
Release : 2019-09-02
Category : Mathematics
ISBN : 9783110603996
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.
Author : Gerhard Rosenberger,Annika Schürenberg,Leonard Wienke
Publisher : Unknown
Page : 0 pages
File Size : 52,7 Mb
Release : 2024-08-05
Category : Mathematics
ISBN : 3111139514
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
Author : Steven Howard Weintraub
Publisher : World Scientific
Page : 438 pages
File Size : 50,7 Mb
Release : 2022-05-25
Category : Mathematics
ISBN : 9789811246685
This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
Author : Ian Stewart
Publisher : CRC Press
Page : 418 pages
File Size : 41,6 Mb
Release : 1990-05-15
Category : Mathematics
ISBN : 9781135439125
Galois theory is a fascinating mixture of classical and modern mathematics, and in fact provided much of the seed from which abstract algebra has grown. It is a showpiece of mathematical unification and of "technology transfer" to a range of modern applications. Galois Theory, Second Edition is a revision of a well-established and popular te
Author : G. P Hochschild
Publisher : Unknown
Page : 284 pages
File Size : 49,8 Mb
Release : 1981-06-30
Category : Electronic
ISBN : 1461381150