Download or read book The Structure and Applications of Galois Algebras written by Thomas Francis Noonan and published by . This book was released on 1971 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report describes a general Galois algebra and discusses some of its applications.
Download or read book Abstract Algebra written by Celine Carstensen and published by Walter de Gruyter. This book was released on 2011 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Abstract Algebra written by Gerhard Rosenberger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-08-05 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Abstract Algebra written by Celine Carstensen-Opitz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Abstract Algebra written by Stephen Lovett and published by CRC Press. This book was released on 2015-07-13 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Discovery-Based Approach to Learning about Algebraic StructuresAbstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester int
Download or read book Galois Connections and Applications written by K. Denecke and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint situation" is that information about objects and relationships in one of the two worlds may be used to gain new information about the other world, and vice versa. In classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Or, in algebraic geometry, a good knowledge of polynomial rings gives insight into the structure of curves, surfaces and other algebraic vari eties, and conversely. Moreover, restriction to the "Galois-closed" or "Galois-open" objects (the fixed points of the composite maps) leads to a precise "duality between two maximal subworlds".
Download or read book Galois Theory written by Ian Stewart and published by CRC Press. This book was released on 1990-05-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Download or read book Foundations of Galois Theory written by M. M. Postnikov and published by Courier Corporation. This book was released on 2004-02-02 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. The source of modern abstract algebra and one of abstract algebra's most concrete applications, Galois theory serves as an excellent introduction to group theory and provides a strong, historically relevant motivation for the introduction of the basics of abstract algebra. This two-part treatment begins with the elements of Galois theory, focusing on related concepts from field theory, including the structure of important types of extensions and the field of algebraic numbers. A consideration of relevant facts from group theory leads to a survey of Galois theory, with discussions of normal extensions, the order and correspondence of the Galois group, and Galois groups of a normal subfield and of two fields. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n ≥ 5.
Download or read book Galois Theory written by Emil Artin and published by . This book was released on 2020-02 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
Download or read book Galois Theory Hopf Algebras and Semiabelian Categories written by George Janelidze and published by American Mathematical Soc.. This book was released on 2004 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an up-to-date account of the many current connections among Galois theories, Hopf algebras, and semiabeliancategories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures. Articles are suitable for graduate students and researchers,specifically those interested in Galois theory and Hopf algebras and their categorical unification.
Download or read book Algebra written by Falko Lorenz and published by Springer Science & Business Media. This book was released on 2006-07-02 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.
Download or read book Inverse Galois Theory written by Gunter Malle and published by Springer. This book was released on 2018-07-27 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.
Download or read book Taming Wild Extensions Hopf Algebras and Local Galois Module Theory written by Lindsay Childs and published by American Mathematical Soc.. This book was released on 2000 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree p and p2; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.
Download or read book Hopf Algebras and Galois Theory written by Stephen U. Chase and published by Springer. This book was released on 2007-01-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Galois Theory written by Mikhail Mikhaĭlovich Postnikov and published by Pergamon. This book was released on 1962 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. The source of modern abstract algebra and one of abstract algebra's most concrete applications, Galois theory serves as an excellent introduction to group theory and provides a strong, historically relevant motivation for the introduction of the basics of abstract algebra. This two-part treatment begins with the elements of Galois theory, focusing on related concepts from field theory, including the structure of important types of extensions and the field of algebraic numbers. A consideration of relevant facts from group theory leads to a survey of Galois theory, with discussions of normal extensions, the order and correspondence of the Galois group, and Galois groups of a normal subfield and of two fields. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n [greater than or equal] 5. Book jacket.
Download or read book Extending Structures written by Ana Agore and published by CRC Press. This book was released on 2019-08-29 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extending Structures: Fundamentals and Applications treats the extending structures (ES) problem in the context of groups, Lie/Leibniz algebras, associative algebras and Poisson/Jacobi algebras. This concisely written monograph offers the reader an incursion into the extending structures problem which provides a common ground for studying both the extension problem and the factorization problem. Features Provides a unified approach to the extension problem and the factorization problem Introduces the classifying complements problem as a sort of converse of the factorization problem; and in the case of groups it leads to a theoretical formula for computing the number of types of isomorphisms of all groups of finite order that arise from a minimal set of data Describes a way of classifying a certain class of finite Lie/Leibniz/Poisson/Jacobi/associative algebras etc. using flag structures Introduces new (non)abelian cohomological objects for all of the aforementioned categories As an application to the approach used for dealing with the classification part of the ES problem, the Galois groups associated with extensions of Lie algebras and associative algebras are described
