Quasi-Frobenius Rings and Generalizations PDF Download

Author: H. Tachikawa
Publisher: Springer
ISBN: 354037812X
Category : Mathematics
Languages : en
Pages : 184

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Book Description
As each animal unbuttons its buttons another animal appears.

Author: W. K. Nicholson
Publisher: Cambridge University Press
ISBN: 9780521815932
Category : Mathematics
Languages : en
Pages : 332

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Book Description
Provides an elementary account of the basic facts about quasi-Frobenius rings.

Author: R. V. Gamkrelidze
Publisher: Springer Science & Business Media
ISBN: 1475705077
Category : Mathematics
Languages : en
Pages : 259

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Book Description
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 . . . . . . . . .

Author: Kiyoshi Igusa
Publisher: American Mathematical Soc.
ISBN: 0821891405
Category : Mathematics
Languages : en
Pages : 236

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Book Description
This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams.

Author: Carl Faith
Publisher: Cambridge University Press
ISBN: 9780521277389
Category : Mathematics
Languages : en
Pages : 180

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Book Description
This work includes all known theorems on the subject of noncommutative FPF rings.

Author: Adnan Tercan
Publisher: Birkhäuser
ISBN: 3034809522
Category : Mathematics
Languages : en
Pages : 389

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Book Description
The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.

Author: Hidetoshi Marubayashi
Publisher: World Scientific
ISBN: 9812818332
Category : Mathematics
Languages : en
Pages : 314

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Book Description
This volume consists of a collection of survey articles by invited speakers and original articles refereed by world experts that was presented at the fifth ChinaOCoJapanOCoKorea International Symposium. The survey articles provide some ideas of the application as well as an excellent overview of the various areas in ring theory. The original articles exhibit new ideas, tools and techniques needed for successful research investigation in ring theory and show the trend of current research."

Author: Dinh Van Huynh
Publisher: American Mathematical Soc.
ISBN: 0821887971
Category : Mathematics
Languages : en
Pages : 330

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Book Description
This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.

Author: Robert Gordon
Publisher: Elsevier
ISBN: 1483274152
Category : Mathematics
Languages : en
Pages : 396

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Book Description
Ring Theory provides information pertinent to the fundamental aspects of ring theory. This book covers a variety of topics related to ring theory, including restricted semi-primary rings, finite free resolutions, generalized rational identities, quotient rings, idealizer rings, identities of Azumaya algebras, endomorphism rings, and some remarks on rings with solvable units. Organized into 24 chapters, this book begins with an overview of the characterization of restricted semi-primary rings. This text then examines the case where K is a Hensel ring and A is a separable algebra. Other chapters consider establishing the basic properties of the four classes of projective modules, with emphasis on the finitely generated case. This book discusses as well the non-finitely generated cases and studies infinitely generated projective modules. The final chapter deals with abelian groups G that are injective when viewed as modules over their endomorphism rings E(G). This book is a valuable resource for mathematicians.

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 1402051417
Category : Mathematics
Languages : en
Pages : 405

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Book Description
This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.