f-Clean Rings Relative to Right Ideals

  • 27 Jan 2024
  • Published Resarch - Mathematics


Hamza Hakmi and Rahaf Al-Dakkak

Published in

Palestine Journal of Mathematics, volume 11, No. 4, pp. 68-80, December 2022.



An element a of associative ring R with identity is called full if sat = 1 for some s, t ∈ R. A ring R is called f−clean ring if every element of R is the sum of a full and an idempotent. In this paper, we introduce the concept of f−clean ring relative to right ideal. We study various properties of this ring. We give some relations between f−clean rings and f−clean rings of 2×2 matrices over R, relative to some right ideal . New characterization obtained include necessary and sufficient conditions of a ring R to be f−clean in terms P−local and P−clean rings. Also, We proved that every ring is f− clean relative to any maximal right ideal of it.

Keywords: (P −) idempotent, Clean, P −clean ring, Full elements, f−clean ring, f−clean ring relative to right ideal.

Link to full paper