ON QUASI-COMMUTATIVE RINGS

被引：1

作者：

Jung, Da Woon ^{[1
]}

Kim, Byung-Ok ^{[2
]}

Kim, Hong Kee ^{[3
]}

Lee, Yang ^{[4
]}

Nam, Sang Bok ^{[5
]}

Ryu, Sung Ju ^{[1
]}

Sung, Hyo Jin ^{[1
]}

Yun, Sang Jo ^{[1
]}

机构：

[1] Pusan Natl Univ, Dept Math, Pusan 609735, South Korea

[2] Korea Sci Acad, Dept Math, Pusan 614103, South Korea

[3] Gyeongsang Natl Univ, Dept Math & Rins, Jinju 660701, South Korea

[4] Pusan Natl Univ, Dept Math Educ, Pusan 609735, South Korea

[5] Kyungdong Univ, Dept Early Child Educ, Kosung 219830, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2016年 / 53卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

quasi-commutative ring; polynomial ring; central element; radical; ARMENDARIZ RINGS;

D O I：

10.4134/JKMS.2016.53.2.475

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：475 / 488

页数：14

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