Strongly weak idempotent nil -clean rings

Articles in Press

Document Type : Research Paper

Authors

1 Department of Computer Science and Systems Engineering, College of Engineering, Andhra University, Visakhapatnam, Andhra Pradesh, India

2 Department of Mathematics, Addis Ababa University, Addis Ababa

3 Department of Mathematics , Addis Ababa University

Abstract

We introduce the concept of strongly weak idempotent nil-clean rings which is a generalization of strongly weakly nil clean rings. We characterize strongly weak idempotent nil-clean rings in terms of the set of nilpotent elements, homomorphic images, and Jacobson radicals. We prove that a ring R is strongly weak idempotent nil-clean if and only if for any a∈R, a−a3 is nilpotent if and only if Nil(R) forms an ideal and R/Nil(R) is reduced weak idempotent nil-clean if and only if R has no homomorphic image Z3⊕Z3 and a2−a4 is nilpotent. Moreover, we prove that a strongly weak idempotent nil-clean ring R with 2∈J(R) satisfies nil-involution property.

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Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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