Some characterizations of the maximal ZG-regular ideal in a ring

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Document Type : Research Paper

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Department of Mathematices, Islamic Azad University, Roudehen Branch, Roudehen, Tehran, Iran.

Abstract

Let R be an associative ring with identity. A ring R is called ZG-regular( resp. strongly ZG-regular) if, for every a in R, there exist positive integer n and g in G, such that ang ∈a^ngRa^ng (resp. a^ng ∈a^(n+1)gR. In this paper, we shall show that the join of all ZG-regular ideals in an arbitrary ring R is a ZG-regular ideal, and so there exists a unique maximal ZG-regular ideal M = M(R) in R, whose structure we investigate. Furthermore, we establish the necessary and sufficient condition for a ring to be a direct sum of its ideals.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 24 September 2025

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