Journal of Advances in Mathematics and Computer Science

On Rings where Certain Subsets are Multiplicatively Generated by Idempotents

Hazar Abu-Khuzam *

Department of Mathematics, American University of Beirut, Beirut, Lebanon.

*Author to whom correspondence should be addressed.

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Abstract

In a Boolean ring, every element is trivially multiplicatively generated by idempotent elements. In this paper, we study the structure of rings in which certain subsets are multiplicatively generated by idempotents or multiplicatively generated by idempotents and nilpotents.

Keywords: Jacobson radical, commutator ideal, artinian ring, semisimple ring

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