TY - JOUR
T1 - On Quasi-cofaithful Ideals
TT - ایدآل های شبه هم صادق
JF - jsci
JO - jsci
VL - 11
IS - 2
UR - http://jsci.khu.ac.ir/article-1-1441-en.html
Y1 - 2011
SP - 183
EP - 194
KW - 1- zip rings
KW - 2- quasi-Baer rings
KW - 3- quasi-Armendariz rings
KW - 4- u.p.-monoids
KW - 5- cofaithful ideals
N2 - We introduce quasi-cofaithful ideals which is a generalization of cofaithful ideals, and investigate their properties. We say a faithful ideal $I$ is textit{quasi-cofaithful} if $I$ contains a finitely generated faithful ideal $I_1$. We show that every faithful ideal of $R$ is quasi-cofaithful if and only if every faithful ideal of $M_n(R)$ is quasi-cofaithful. We show that if $R$ has the descending chain condition on right annihilators of right ideals, then each faithful ideal of $R$ is quasi-cofaithful. For a u.p.-monoid $M$, it is shown that if $R$ is a quasi-Baer ring, then each faithful ideal of $R$ is quasi-cofaithful if and only if each faithful ideal of monoid ring $R[M]$ is quasi-cofaithful.
M3
ER -