Open AccessSemicommutativity of rings by the way of idempotents
Author(s) -
Handan Köse,
Burcu Üngör,
Abdullah Harmancı
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1911497k
Subject(s) - mathematics , idempotence , von neumann regular ring , noncommutative ring , pure mathematics , ring (chemistry) , class (philosophy) , primitive ring , principal ideal ring , combinatorics , commutative ring , commutative property , computer science , chemistry , organic chemistry , artificial intelligence
In this paper, we focus on the semicommutative property of rings via idempotent elements. In this direction, we introduce a class of rings, so-called right e-semicommutative rings. The notion of right e-semicommutative rings generalizes those of semicommutative rings, e-symmetric rings and right e-reduced rings. We present examples of right e-semicommutative rings that are neither semicommutative nor e-symmetric nor right e-reduced. Some extensions of rings such as Dorroh extensions and some subrings of matrix rings are investigated in terms of right e-semicommutativity. We prove that if R is a right e-semicommutative clean ring, then the corner ring eRe is clean.