Completely Regular Generalized Adjoint Semigroups
Xie Jing-ran · Journal of Jilin University(Science Edition) · 2009
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 M(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.