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Author: Simeon Ivanov
Publisher: American Mathematical Soc.
Published: 1992
Total Pages: 290
ISBN-13: 9780821831403
DOWNLOAD EBOOK →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: Gerhard Rosenberger
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2024-08-05
Total Pages: 422
ISBN-13: 3111142523
DOWNLOAD EBOOK →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: Victor Percy Snaith
Publisher: World Scientific
Published: 2003
Total Pages: 234
ISBN-13: 9789812386007
DOWNLOAD EBOOK →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: Grégory Berhuy
Publisher: Cambridge University Press
Published: 2010-09-09
Total Pages: 328
ISBN-13: 1139490885
DOWNLOAD EBOOK →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
Publisher: American Mathematical Soc.
Published: 1969
Total Pages: 87
ISBN-13: 0821812521
DOWNLOAD EBOOK →Author: Victor P Snaith
Publisher: World Scientific Publishing Company
Published: 2003-09-29
Total Pages: 228
ISBN-13: 9813102233
DOWNLOAD EBOOK →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
Publisher: Walter de Gruyter
Published: 2011
Total Pages: 381
ISBN-13: 311025008X
DOWNLOAD EBOOK →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
Publisher: American Mathematical Soc.
Published: 2011-10-06
Total Pages: 234
ISBN-13: 0821872885
DOWNLOAD EBOOK →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: Mohamed Ayad
Publisher: World Scientific Publishing Company
Published: 2018-04-26
Total Pages: 452
ISBN-13: 9813238321
DOWNLOAD EBOOK →Author: Siegfried Bosch
Publisher: Springer
Published: 2018-11-02
Total Pages: 352
ISBN-13: 3319951777
DOWNLOAD EBOOK →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.
