Download or read book Locally Strongly Separable Algebras Over Connected Commutative Rings written by John Frederick Yeagley and published by . This book was released on 1972 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Separable Galois Theory of Commutative Rings written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n

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 Publicationes mathematicae written by Kossuth Lajos Tudományegyetem. Matematikai Intézet and published by . This book was released on 1975 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book American Doctoral Dissertations written by and published by . This book was released on 1972 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Separable Galois Theory of Commutative Rings Second Edition written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Galois Theories written by Francis Borceux and published by Cambridge University Press. This book was released on 2001-02-22 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.

Download or read book Algebra and Geometry written by R. V. Gamkrelidze and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains five review articles, three in the Al gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differential-geometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 1965-1968. v CONTENTS ALGEBRA RING THEORY L. A. Bokut', K. A. Zhevlakov, and E. N. Kuz'min § 1. Associative Rings. . . . . . . . . . . . . . . . . . . . 3 § 2. Lie Algebras and Their Generalizations. . . . . . . 13 ~ 3. Alternative and Jordan Rings. . . . . . . . . . . . . . . . 18 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 MODULES A. V. Mikhalev and L. A. Skornyakov § 1. Radicals. . . . . . . . . . . . . . . . . . . 59 § 2. Projection, Injection, etc. . . . . . . . . . . . . . . . . . . 62 § 3. Homological Classification of Rings. . . . . . . . . . . . 66 § 4. Quasi-Frobenius Rings and Their Generalizations. . 71 § 5. Some Aspects of Homological Algebra . . . . . . . . . . 75 § 6. Endomorphism Rings . . . . . . . . . . . . . . . . . . . . . 83 § 7. Other Aspects. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 91 LATTICE THEORY M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. Identity and Defining Relations in Lattices . . . . . . 120 § 3. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § 4. Geometrical Aspects and the Related Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • 125 § 5. Homological Aspects. . . . . . . . . . . . . . . . . . . . . . 129 § 6. Lattices of Congruences and of Ideals of a Lattice . . 133 § 7. Lattices of Subsets, of Subalgebras, etc. . . . . . . . . 134 § 8. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 § 9. Topological Aspects. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered Sets. . . . . . . . . . . . . . . . . . . . 141 § 11. Other Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY INTEGRAL GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .

Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1974 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains articles of significant interest to mathematicians, including reports on current mathematical research.

Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1989 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Comprehensive Dissertation Index Mathematics Statistics Physics A E written by and published by . This book was released on 1984 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transactions of the American Mathematical Society written by and published by . This book was released on 1972 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Index and Other Useful Information written by A. Dold and published by Springer. This book was released on 2013-12-11 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1975 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modules and Algebras written by Robert Wisbauer and published by CRC Press. This book was released on 1996-05-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.