Strongly nil *-clean rings

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Abdullah Harmancı¹  Huanyin Chen¹  A. Çiğdem Özcan² 

[1] Hacettepe University, Department of Mathematics;Hangzhou Normal University, Department of Mathematics

关键词: Rings with involution;    Strongly nil ∗-clean ring;    ∗-Boolean ring;    Boolean ring;   

DOI  :  10.13069/jacodesmath.284954

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

A ∗-ring R is called strongly nil ∗-clean if every element of R is the sum of a projection and a nilpotentelement that commute with each other. In this paper we investigate some properties of strongly nil ∗-rings and prove that R is a strongly nil ∗-clean ring if and only if every idempotent in R is a projection,R is periodic, and R/J(R) is Boolean. We also prove that a ∗-ring R is commutative, strongly nil∗-clean and every primary ideal is maximal if and only if every element of R is a projection.

【 授权许可】

CC BY