Title: The Basic Ring-Theoretic Notions and Their Characterizations
Abstract: Publisher SummaryThe chapter discusses the basic ring-theoretic notions and their characterizations. A ring R is left Artinian if R satisfies the descending chain condition (DCC or, equivalently, the minimum condition) on left ideals. A ring R is simple Artinian if R is a simple ring that is left Artinian. A ring R is semi-simple (Artinian) if it satisfies certain properties and is the most important kind of ring. A ring R is left Noetherian if R satisfies the ascending chain condition (ACC or equivalently the maximum condition) on left ideals. A ring R is primitive if R has a faithful simple module. The Jacobson radical Jac(R) is the intersection of the primitive ideals of R. With each notion, the chapter mentions many characterizations.
Publication Year: 1988
Publication Date: 1988-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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