Revisiting J-semicommutative rings

Tikaram Subedi () and Debraj Roy ()
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Tikaram Subedi: National Institute of Technology Meghalaya
Debraj Roy: National Institute of Technology Meghalaya

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1222-1229

Abstract: Abstract Let J(R) denote the Jacobson radical of a ring R. R is called J-semicommutative if for any $$a,b\in R, ab=0$$ a , b ∈ R , a b = 0 implies $$aRb\subseteq J(R)$$ a R b ⊆ J ( R ) . We observe that the class of J -semicommutative rings contains the class of left (right) quasi-duo rings and various existing versions of semicommutative rings, symmetric rings and reversible rings. We provide some conditions for J-semicommutative rings to be left quasi-duo. Finally, the consequences of J-semicommutativity conditions over some classes of rings are discussed.

Keywords: Semicommutative ring; Jacobson radical; J-semicommutative ring; 13C99; 16D80; 16U80 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-024-00562-y

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