Feebly r-clean ring and feebly*-r-clean ring
DOI:
https://doi.org/10.23755/rm.v48i0.1144Keywords:
r-Clean rings, feebly r-clean ring, *-clean ring, feebly *-clean ring, *-r- feebly clean ring.Abstract
In this article, we introduce the concept of feebly r-clean ring and feebly ∗-r-clean ring. A ring R is defined to be feebly r-clean, if every element a can be written as a = r + e − f, where u is a regular and e, f are orthogonal idempotents and A ∗ ring R is defined to be feebly ∗-r clean if every element a can be written as a = r + p − q, where r is regular element and p, q are orthogonal projections. Further we generalise this concept of feebly r-clean ring to feebly g(x)−r-clean ring, where g(x) ∈ C(R)[x] and C(R) is the centre of ring R.
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