The Maximal Semiregular Ideal of Rings and Group Rings

The existence of a unique maximal semiregular ideal, S(R) in a ring R, in which idempotents modulo Jacobson radical J(R), can be lifted, is established. Radical like properties of S(R) are obtained. In particular, for group algebras R = K[G], properties of S(K[G]) and its relations with the Brown-McCoy radical M(K[G]) also have been obtained.