ON 𝒯-NONCOSINGULAR MODULES
نویسندگان
چکیده
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 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 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 کاملT-dual Rickart modules
We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2009
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972709000409