RT - Journal Article
T1 - On Quasi-cofaithful Ideals
JF - jsci
YR - 2011
JO - jsci
VO - 11
IS - 2
UR - http://jsci.khu.ac.ir/article-1-1441-en.html
SP - 183
EP - 194
K1 - 1- zip rings
K1 - 2- quasi-Baer rings
K1 - 3- quasi-Armendariz rings
K1 - 4- u.p.-monoids
K1 - 5- cofaithful ideals
AB - 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.
LA eng
UL http://jsci.khu.ac.ir/article-1-1441-en.html
M3
ER -