Abstract：The unit-regularity of a ring with identity is studied. When R is a ring with identity,the unit-regularity of a ring R is
characterzed and it is proved that the unit-regularity of R is equivalent to that of the full matrix ringMn(R ).For a completely 0-simple semigroup ring S = M0(G; I;Λ; P) with|I|=|Λ|<+ ∞ and invertible P ,
the unit-regularity of R S is characterized.
