完全正则的广义圈乘半群

Completely Regular Generalized Adjoint Semigroups

刻画具有完全正则的广义圈乘半群的环.证明了环R有一个广义圈乘半群R◇是群之并当且仅当R◇同构于一个Morita contextM(S,T,U,V)的由E11诱导的广义圈乘半群,其中S是广义根环,T是强正则环,VU=0,并且对于S的任意幂等元e,都有eU=Ve=0.

Rings with a completely regular generalized adjoint semigroup are characterized. It is proved that a generalized adjoint semigroup R° of a ring R is a union of groups if and only if R° is isomorphic to the generalized adjoint semigroup induced by E11 of a Morita context М（S, T, U, V）, where S is a generalized radical ring, T is a strongly regular ring, VU =0, and eU = Ve =0 for any idempotent e ∈ S.