Abstract
Multiplicative semigroups of rings form an important class of semigroups and one theme in the study of semigroups is how the structure of this semigroup affects the structure of the ring. An important tool in analyzing the structure of a semigroup is the Green’s relations. We study some properties of these relations on the multiplicative semigroup of a regular ring with unity. This also gives easier proofs of some known results on ring theory.
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