The Armendariz property on ideals

JOURNAL OF ALGEBRA

卷:354

Article

Kwak, Tai Keun¹  Lee, Yang²  Yun, Sang Jo³ 

[1] Daejin Univ, Dept Math, Pochon 487711, South Korea

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

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

关键词: Ideal-Armendariz ring;    Armendariz ring;    Insertion-of-factors-property (IFP);    Symmetric ring;    Von Neumann regular ring;    Minimal noncommutative ring;    Abelian ring;   

DOI  :  10.1016/j.jalgebra.2011.12.019

来源: Elsevier

【 摘 要 】

In the present note we study the Armendariz property on ideals of rings, introducing a new concept which unifies the Armendariz property and the insertion-of-factors-property (simply. IFP) for rings. In relation with this work, we investigate rings over which polynomial rings are IFP, called strongly IFP rings, which generalize both ideal-Armendariz rings and strongly reversible rings. The classes of minimal noncommutative ideal-Armendariz rings and strongly IFP rings, and the classes of minimal non-Abelian ideal-Armendariz rings and strongly IFP rings are completely determined, up to isomorphism. It is also shown that a local ring is Armendariz. symmetric, and strongly reversible (hence ideal-Armendariz) when the cardinality of the Jacobson radical is 4. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free