Structure of Rings

Structure of Rings
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
Total Pages: 311
Release: 1964
Genre: Mathematics
ISBN: 0821810375

The main purpose of this volume is to give an account of the important developments in the theory of (non-commutative) rings. These are: the structure theory of rings without finiteness assumptions, cohomology of algebras, and structure and representation theory of non-semi-simple rings (Frobenius algebras, quasi-Frobenius rings).

The Algebraic Structure of Group Rings

The Algebraic Structure of Group Rings
Author: Donald S. Passman
Publisher: Courier Corporation
Total Pages: 754
Release: 2011-01-01
Genre: Mathematics
ISBN: 0486482065

"'Highly recommended' by the Bulletin of the London Mathematical Society, this book offers a comprehensive, self-contained treatment of group rings. The subject involves the intersection of two essentially different disciplines, group theory and ring theory. The Bulletin of the American Mathematical Society hailed this treatment as 'a majestic account,' proclaiming it "encyclopedic and lucid." 1985 edition"--

Cyclic Modules and the Structure of Rings

Cyclic Modules and the Structure of Rings
Author: S.K. Jain
Publisher: Oxford University Press
Total Pages: 231
Release: 2012-09-27
Genre: Mathematics
ISBN: 019966451X

This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.

The Theory of Rings

The Theory of Rings
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
Total Pages: 160
Release: 1943-12-31
Genre: Mathematics
ISBN: 0821815024

The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.

Finite Commutative Rings and Their Applications

Finite Commutative Rings and Their Applications
Author: Gilberto Bini
Publisher: Springer Science & Business Media
Total Pages: 181
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461509572

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Rings and Categories of Modules

Rings and Categories of Modules
Author: Frank W. Anderson
Publisher: Springer Science & Business Media
Total Pages: 386
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461244188

This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.

The Cambridge Guide to Homer

The Cambridge Guide to Homer
Author: Corinne Ondine Pache
Publisher: Cambridge University Press
Total Pages: 974
Release: 2020-03-05
Genre: Literary Collections
ISBN: 1108663621

From its ancient incarnation as a song to recent translations in modern languages, Homeric epic remains an abiding source of inspiration for both scholars and artists that transcends temporal and linguistic boundaries. The Cambridge Guide to Homer examines the influence and meaning of Homeric poetry from its earliest form as ancient Greek song to its current status in world literature, presenting the information in a synthetic manner that allows the reader to gain an understanding of the different strands of Homeric studies. The volume is structured around three main themes: Homeric Song and Text; the Homeric World, and Homer in the World. Each section starts with a series of 'macropedia' essays arranged thematically that are accompanied by shorter complementary 'micropedia' articles. The Cambridge Guide to Homer thus traces the many routes taken by Homeric epic in the ancient world and its continuing relevance in different periods and cultures.

Saturn from Cassini-Huygens

Saturn from Cassini-Huygens
Author: Michele Dougherty
Publisher: Springer Science & Business Media
Total Pages: 799
Release: 2009-09-30
Genre: Science
ISBN: 1402092172

This book is one of two volumes meant to capture, to the extent practical, the scienti?c legacy of the Cassini-Huygens prime mission, a landmark in the history of planetary exploration. As the most ambitious and interdisciplinary planetary exploration mission ?own to date, it has extended our knowledge of the Saturn system to levels of detail at least an order of magnitude beyond that gained from all previous missions to Saturn. Nestled in the brilliant light of the new and deep understanding of the Saturn planetary system is the shiny nugget that is the spectacularly successful collaboration of individuals, - ganizations and governments in the achievement of Cassini-Huygens. In some ways the pa- nershipsformedandlessonslearnedmaybethemost enduringlegacyofCassini-Huygens.The broad, international coalition that is Cassini-Huygens is now conducting the Cassini Equinox Mission and planning the Cassini Solstice Mission, and in a major expansion of those fruitful efforts, has extended the collaboration to the study of new ?agship missions to both Jupiter and Saturn. Such ventures have and will continue to enrich us all, and evoke a very optimistic vision of the future of international collaboration in planetary exploration. The two volumes in the series Saturn from Cassini-Huygens and Titan from Cassini- Huygens are the direct products of the efforts of over 200 authors and co-authors. Though each book has a different set of three editors, the group of six editors for the two volumes has worked together through every step of the process to ensure that these two volumes are a set.

Three Rings

Three Rings
Author: Daniel Mendelsohn
Publisher: New York Review of Books
Total Pages: 129
Release: 2022-04-26
Genre: Biography & Autobiography
ISBN: 1681376393

A memoir, biography, work of history, and literary criticism all in one, this moving book tells the story of three exiled writers—Erich Auerbach, François Fénelon, and W. G. Sebald—and their relationship with the classics, from Homer to Mimesis. In a genre-defying book hailed as “exquisite” (The New York Times) and “spectacular” (The Times Literary Supplement), the best-selling memoirist and critic Daniel Mendelsohn explores the mysterious links between the randomness of the lives we lead and the artfulness of the stories we tell. Combining memoir, biography, history, and literary criticism, Three Rings weaves together the stories of three exiled writers who turned to the classics of the past to create masterpieces of their own—works that pondered the nature of narrative itself: Erich Auerbach, the Jewish philologist who fled Hitler’s Germany and wrote his classic study of Western literature, Mimesis, in Istanbul; François Fénelon, the seventeenth-century French archbishop whose ingenious sequel to the Odyssey, The Adventures of Telemachus—a veiled critique of the Sun King and the best-selling book in Europe for a hundred years—resulted in his banishment; and the German novelist W.G. Sebald, self-exiled to England, whose distinctively meandering narratives explore Odyssean themes of displacement, nostalgia, and separation from home. Intertwined with these tales of exile and artistic crisis is an account of Mendelsohn’s struggle to write two of his own books—a family saga of the Holocaust and a memoir about reading the Odyssey with his elderly father—that are haunted by tales of oppression and wandering. As Three Rings moves to its startling conclusion, a climactic revelation about the way in which the lives of its three heroes were linked across borders, languages, and centuries forces the reader to reconsider the relationship between narrative and history, art and life.