Volume 11, Issue 2 (2-2011)
2011, 11(2): 183-194 |
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Abstract: (4685 Views)
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.
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.
Keywords: 1- zip rings, 2- quasi-Baer rings, 3- quasi-Armendariz rings, 4- u.p.-monoids, 5- cofaithful ideals
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