ABSTRACT
In this article, we prove that a regular ring R is one-sided unit-regular if and only if there exists a full idempotent e ∈ R such that eRe is one-sided unit-regular. Furthermore, we prove that a regular ring R is one-sided unit-regular if and only if for all full a,b ∈ R, implies that there exists a right or left invertible u ∈ R such that au = ub if and only if R = A 1 ⊕ B = A 2 ⊕ C with progenerators A 1 ≅ A 2 implies that B ≲ C or C ≲ B.
Notes
Communicated by V. Artamonov.