ON QUASI-COMMUTATIVE RINGS

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...

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Published inJournal of the Korean Mathematical Society Vol. 53; no. 2; pp. 475 - 488
Main Authors Jung, Da Woon, Kim, Byung-Ok, Kim, Hong Kee, Lee, Yang, Nam, Sang Bok, Ryu, Sung Ju, Sung, Hyo Jin, Yun, Sang Jo
Format Journal Article
LanguageKorean
Published 2016
Subjects
radical
quasi-commutative ring
central element
polynomial ring
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO201609562999056
ISSN:0304-9914