摘要
In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or A is finite,in Section 2,the regularity of the Munn ring M(R;I,A;P)is characterized;in Section 3,for a completely 0-simple semigroup S= M°(G;I,A;P),the regularity of RS is characterized.Meantime,the author shows that for a locally finite monoid S and a ring R with identity,RS is a strong IBN ring if and only if R is so;RS is fully Dedekind-finite if and only if R is so.
In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or A is finite,in Section 2,the regularity of the Munn ring M(R;I,A;P)is characterized;in Section 3,for a completely 0-simple semigroup S= M°(G;I,A;P),the regularity of RS is characterized.Meantime,the author shows that for a locally finite monoid S and a ring R with identity,RS is a strong IBN ring if and only if R is so;RS is fully Dedekind-finite if and only if R is so.
