منابع مشابه
Strongly noncosingular modules
An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...
متن کاملSome Results on Local Cohomology Modules
Let R be a commutative Noetherian ring, a an ideal of R, and let M be a finitely generated R-module. For a non-negative integer t, we prove that H a(M) is a-cofinite whenever H t a(M) is Artinian and H i a(M) is a-cofinite for all i < t. This result, in particular, characterizes the a-cofiniteness property of local cohomology modules of certain regular local rings. Also, we show that for a loca...
متن کاملOn the decomposition of noncosingular $sum$-lifting modules
Let $R$ be a right artinian ring or a perfect commutativering. Let $M$ be a noncosingular self-generator $sum$-liftingmodule. Then $M$ has a direct decomposition $M=oplus_{iin I} M_i$,where each $M_i$ is noetherian quasi-projective and eachendomorphism ring $End(M_i)$ is local.
متن کاملstrongly noncosingular modules
an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...
متن کاملRESULTS ON ALMOST COHEN-MACAULAY MODULES
Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2014
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1302-52