A Galois Theory Of Linear Systems Over Commutative Fields
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A Galois Theory Of Linear Systems Over Commutative Fields
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Author : Reinhold Baer
language : en
Publisher:
Release Date : 1940
A Galois Theory Of Linear Systems Over Commutative Fields written by Reinhold Baer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with categories.
Linear Groups With An Exposition Of Galois Field Theory
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Author : Leonard Eugene Dickson
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-04-01
Linear Groups With An Exposition Of Galois Field Theory written by Leonard Eugene Dickson and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-01 with Mathematics categories.
This classic in the field of abstract algebra has been called "the first systematic treatment of finite fields in the mathematical literature." Divided into two sections-"Introduction to the Galois Field Theory" and "Theory of Linear Groups in a Galois Field"-and crammed with examples and theorems, Linear Groups remains relevant more than a century after its publication. Learn about: . definition and properties of finite fields . classification and determination of irreducible quantics . miscellaneous properties of Galois Fields . analytic representation of substitutions on the marks of a Galois Field . the Abelian linear group . the hyperabelian group . the hyperorthogonal and related linear groups . and much more. This historic contribution to the theory of groups is still appreciated by mathematicians today. American mathematician LEONARD EUGENE DICKSON (1874-1954) received the University of Chicago's first doctorate in mathematics, and later taught there for 39 years. His published works include Linear Algebras (1914), History of the Theory of Numbers (1919-23), and Studies in the Theory of Numbers (1930).
Galois Theory
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Author : Emil Artin
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01
Galois Theory written by Emil Artin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications. The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more. Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.
Algebraic Groups And Differential Galois Theory
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Author : Teresa Crespo
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Algebraic Groups And Differential Galois Theory written by Teresa Crespo 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 2011 with Computers categories.
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.
Linear Systems Over Commutative Rings
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Author : James W. Brewer
language : en
Publisher: CRC Press
Release Date : 1986-04-22
Linear Systems Over Commutative Rings written by James W. Brewer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-04-22 with Mathematics categories.
Galois Theory
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Author : Steven H. Weintraub
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
Galois Theory written by Steven H. Weintraub 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 2008-10-20 with Mathematics categories.
Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.
Galois Theory And Advanced Linear Algebra
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Author : Rajnikant Sinha
language : en
Publisher: Springer Nature
Release Date : 2019-12-28
Galois Theory And Advanced Linear Algebra written by Rajnikant Sinha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-28 with Mathematics categories.
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
The Separable Galois Theory Of Commutative Rings Second Edition
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Author : Andy R. Magid
language : en
Publisher: CRC Press
Release Date : 2014-07-14
The Separable Galois Theory Of Commutative Rings Second Edition written by Andy R. Magid and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter on the theory of separable algebras. The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of profinite spaces on which a profinite groupoid acts. It explores how the connection between the categories depends on the construction of a suitable separable closure of the given ring, which in turn depends on certain notions in profinite topology. The book also discusses how to handle rings with infinitely many idempotents using profinite topological spaces and other methods.
Galois Theory Of Algebraic Equations
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Author : Jean-Pierre Tignol
language : en
Publisher: World Scientific Publishing Company
Release Date : 2001-04-02
Galois Theory Of Algebraic Equations written by Jean-Pierre Tignol and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-02 with Mathematics categories.
New Edition available here Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as “group” and “field”. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory. This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters.
Galois Theory
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Author : Ian Stewart
language : en
Publisher: CRC Press
Release Date : 1990-05-15
Galois Theory written by Ian Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-05-15 with Mathematics categories.
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