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Rings and Things and a Fine Array of Twentieth Century Associative Algebra
This book surveys more than 125 years of aspects of associative algebras, especially ring and module theory. It is the first to probe so extensively such a wealth of historical development. Moreover, the author brings the reader up to date, in particular through his report on the subject in the second half of the twentieth century. Included in the book are certain categorical properties from theorems of Frobenius and Stickelberger on the primary decomposition of finite Abelian formulations of the latter by Krull, Goldman, and others; Maschke's theorem on the representation theory of finite groups over a field; and the fundamental theorems of Wedderburn on the structure of finite dimensional ...
Rings, Modules and Representations
The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.
Injective Modules and Injective Quotient Rings
First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)
Injective Modules and Injective Quotient Rings
First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)
Algebra
VI of Oregon lectures in 1962, Bass gave simplified proofs of a number of "Morita Theorems", incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::! mod-B for two rings A and B. Morita's solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a similarity class [AJ in the Brauer group Br(k) of Azumaya algebras over a commutative ring k consists of all algebras B such that the corresponding categories mod-A and mod-B consisting of k-linear morphisms are equivalent by a k-linear functor. (For fields, Br(k) consists of similarity classes of simple ...
Legendary Locals of Covington
Covington was a natural place for people to settle. Located on the banks of the Ohio and Licking Rivers, it developed quickly as the urban core of northern Kentucky. Sitting just opposite of Cincinnati, Ohio, it was a great location for travel by both animals and people. Originally owned by Thomas Kennedy, the land was ultimately purchased by Thomas Carneal and John and Richard Gano, and thus the city of Covington was founded in 1815. Not long after its establishment, railroads made Covington their home and many other businesses followed. By 1850, it was the second-largest city in Kentucky. Over its 200 years, Covington has seen many people play a role in its history, development, and reputation. Some are great business and community leaders. Others made tremendous contributions to the arts, and some are notorious. A community is defined more by its people than its buildings and streets. The individuals who have lived and worked in Covington provide a colorful insight into its past. From its founding until the present day, these individuals are a fascinating look into the citys history.
The Encyclopedia of Northern Kentucky
The Encyclopedia of Northern Kentucky is the authoritative reference on the people, places, history, and rich heritage of the Northern Kentucky region. The encyclopedia defines an overlooked region of more than 450,000 residents and celebrates its contributions to agriculture, art, architecture, commerce, education, entertainment, literature, medicine, military, science, and sports. Often referred to as one of the points of the "Golden Triangle" because of its proximity to Lexington and Louisville, Northern Kentucky is made up of eleven counties along the Ohio River: Boone, Bracken, Campbell, Carroll, Gallatin, Grant, Kenton, Mason, Owen, Pendleton, and Robertson. With more than 2,000 entrie...
Topological Rings
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included.The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.
