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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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发表于 2025-3-21 17:01:39 | 显示全部楼层 |阅读模式
期刊全称A First Course in Noncommutative Rings
影响因子2023T. Y. Lam
视频video
学科分类Graduate Texts in Mathematics
图书封面Titlebook: A First Course in Noncommutative Rings;  T. Y. Lam Textbook 19911st edition Springer-Verlag New York, Inc. 1991 Abstract algebra.Group theo
影响因子One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught 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 basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer­ tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op­ erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathem
Pindex Textbook 19911st edition
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https://doi.org/10.1007/978-1-4684-0406-7Abstract algebra; Group theory; Representation theory; algebra; ring theory
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978-1-4684-0408-1Springer-Verlag New York, Inc. 1991
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Zusammenfassung der Ergebnisse,This chapter will be devoted to the study of two classes of rings, namely, semiperfect rings and left (resp., right) perfect rings. The notion of semiperfect rings is left-right symmetric, while left (resp., right) perfect rings are always semiperfect.
发表于 2025-3-22 13:53:15 | 显示全部楼层
https://doi.org/10.1007/978-3-8274-2736-6wenty years later, E. Noether and E. Artin introduced the Ascending Chain Condition (.) and the Descending Chain Condition (.) as substitutes for finite dimensionality, and Artin proved the analogue of Wedderburn’s Theorem for general semisimple rings. The Wedderburn-Artin theory has since become th
发表于 2025-3-22 17:30:50 | 显示全部楼层
Zusammenfassung und Implikationen, the radical was studied first in the context of nonassociative rings (namely, finite-dimensional Lie algebras) rather than associative rings. In the work of E. Cartan, the radical of a finite-dimensional Lie algebra . (say over ℂ) is defined to be the maximal solvable ideal of .: it is obtained as
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Zusammenfassung und Implikationen,of groups. We have already explained, in the introduction to §6, how ring theory may be brought to bear on group representation theory by viewing representations as modules over group rings. From this viewpoint, many facts in the representation theory and character theory of finite groups can be ded
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Zusammenfassung der Ergebnisse,tivity, so by using exactly the same conditions on rings in general, we can define (and we have defined) the notions of ., and .. However, a little careful thought will show that this is not the only way to generalize the former three classes. In fact, the defining conditions for these classes are c
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