Rings with Morita duality / Weimin Xue
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1523Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1992ISBN: 9783540472834.ISSN: 1617-9692.Sujet MSC : 16D90, Modules, bimodules and ideals in associative algebras, Module categories in associative algebras; module theory in a category-theoretic context; Morita equivalence and duality16S20, Associative rings and algebras arising under various constructions, Centralizing and normalizing extensions
16L30, Associative rings and algebras - Local rings and generalizations, Noncommutative local and semilocal rings, perfect rings
16P20, Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras, Artinian rings and modules
16P40, Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras, Noetherian rings and modulesEn-ligne : Springerlink | Zentralblatt | MathSciNet
... Chapter 1 presents the fundamentals on Morita duality and the approach of B. J. Müller via linear compactness, a most useful tool in the investigation of Morita duality. In the following four chapters the author describes particular rings with duality. Chapter 2 discusses the relation between duality and ring extensions such as finite triangular, normalizing as well as trivial extensions. The classical theory of artinian rings with duality is the content of Chapter 3. Chapter 4 focuses on the problem of Azumaya whether exact rings are selfdual and presents an affirmative answer in the case of locally distributive or artinian duo rings with some additional conditions. In the final part, Chapter 5, noetherian, perfect and quasi-perfect rings with duality are investigated.
The book is well written and can be recommended as an introduction to Morita duality and the techniques used in it. (Zentralblatt)
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