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Titlebook: A First Course in Noncommutative Rings; T. Y. Lam Textbook 19911st edition Springer-Verlag New York, Inc. 1991 Abstract algebra.Group theo

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https://doi.org/10.1007/978-3-8349-9815-6clude all left or right artinian rings. The basic properties of local and semilocal rings are developed, respectively, in §19 and §20. We shall see, for instance, that local rings are connected with the problem of the uniqueness of Krull-Schmidt decompositions, and that semilocal rings are connected with the problem of “cancellation” of modules.
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Textbook 19911st editionught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in ba
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Zusammenfassung der Ergebnisse,onditions on . of a ring. When we move from commutative rings to noncommutative rings, an alternative way of generalizing an “elemenwise” condition should be to replace the role of elements by that of ideals. By making these changes judiciously in the basic definitions, we are led ι the notions of ., and (..
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