Semicommutativity of rings by the way of idempotents | Zendy

Handan Köse | Zendy; Burcu Üngör | Zendy; Abdullah Harmancı | Zendy

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Semicommutativity 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.

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