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Revisiting J-semicommutative rings

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Abstract

Let J(R) denote the Jacobson radical of a ring R. R is called J-semicommutative if for any \(a,b\in R, ab=0\) implies \(aRb\subseteq J(R)\). 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.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Meghalaya, Bijni Complex, Shillong, Meghalaya, 793003, India

    Tikaram Subedi & Debraj Roy

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  1. Tikaram Subedi
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  2. Debraj Roy
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Correspondence to Tikaram Subedi.

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Communicated by B. Sury.

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Subedi, T., Roy, D. Revisiting J-semicommutative rings. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00562-y

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