An extension of the reduced property in rings
Asian-European Journal of Mathematics, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1142/s1793557126500798
- Journal Name: Asian-European Journal of Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Aerospace Database, MathSciNet, zbMATH, Technology Collection (ProQuest)
- Keywords: e-reduced ring, idempotent element, nilpotent element, Reduced ring, Zhou radical
- Hacettepe University Affiliated: Yes
Abstract
Let R be a ring, e2 = e ∈ R and δ(R) stand for the intersection of all essential maximal right ideals of R which is called the Zhou radical. The aim of this paper is to apply the Zhou radical to the e-reducedness of rings. In this direction, a ring R is said to be Zhou right (respectively, left) e-reduced if for any nilpotent a in R, we have ae ∈ δ(R) (respectively, ea ∈ δ(R)). For nonzero idempotents, we investigate properties and supply examples of Zhou right e-reduced rings. Along these lines, we show that right e-semicommutative rings (and so right e-reduced rings and e-symmetric rings), central semicommutative rings and weak symmetric rings are Zhou right e-reduced. As an application, we deal with some extensions of Zhou right e-reduced rings.