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ON QUASI-COMMUTATIVE RINGS
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 Title & Authors
ON QUASI-COMMUTATIVE RINGS
Jung, Da Woon; Kim, Byung-Ok; Kim, Hong Kee; Lee, Yang; Nam, Sang Bok; Ryu, Sung Ju; Sung, Hyo Jin; Yun, Sang Jo;
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 Abstract
We study the structure of central elements in relation with polynomial rings and introduce quasi-commutative as a generalization of commutative rings. The Jacobson radical of the polynomial ring over a quasi-commutative ring is shown to coincide with the set of all nilpotent polynomials; and locally finite quasi-commutative rings are shown to be commutative. We also provide several sorts of examples by showing the relations between quasi-commutative rings and other ring properties which have roles in ring theory. We examine next various sorts of ring extensions of quasi-commutative rings.
 Keywords
quasi-commutative ring;polynomial ring;central element;radical;
 Language
English
 Cited by
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