On Quasi-cofaithful Ideals

We introduce quasi-cofaithful ideals which are a generalization of cofaithful ideals, andinvestigate their properties. we hold that a faithful ideal i is quasi-cofaithful if i containsa finitely generated faithful ideal 1 i . we show that every faithful ideal of r is quasicofaithfulif and only if every faithful ideal of m (r) n is quasi-cofaithful. also we showthat if r has the descending chain condition on right annihilators of right ideals, then eachfaithful ideal of r is quasi-cofaithful. for a u.p.-monoid m, it is shown that if r is aquasi-baer ring, then each faithful ideal of r is quasi-cofaithful if and only if each faithfulideal of the monoid ring r[m] is quasi-cofaithful