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On Weakly K-Clean Rings

Fatemeh Rashedi

Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran

Email address: f-rashedi@tvu.ac.ir

Doi : https://doi.org/10.47013/16.3.8

Cited by : Jordan J. Math & Stat., 16 (3) (2023), 507 - 513

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Received on: July 7, 2022;                                         Accepted on: Oct. 30, 2022

 Abstract. In this paper, we offer a new generalization of the k-clean ring that is called weakly k-clean ring. Let 2 ≤ k ϵ N. Then the ring R is said to be a weakly k-clean if for each a ϵ R there exist u ϵ U(R) and e ϵ Pk(R) such that a = u+e or a = u−e. We obtain some properties of weakly k-clean rings. It is shown that each homomorphic image of a weakly k-clean ring is weakly k-clean. Also, it is proved that the ring R[R, S] is weakly k-clean if and only if R is k-clean and S is weakly k-clean.

Keywords: weakly k-clean ring, k-clean ring.