نتایج جستجو برای: Right strong stably finite ring
تعداد نتایج: 1009013 فیلتر نتایج به سال:
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for the first time nakayama introduced qf-ring. in 1967 carl. faith and elbert a. walker showed that r is qf-ring if and only if each injective right r-module is projective if and only if each injective left r-modules is projective. in 1987 s.k.jain and s.r.lopez-permouth proved that every ring homomorphic images of r has the property that each cyclic s-module is essentialy embeddable in dire...
let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr"{u}fer domains and um$t$ domains in terms of dimension ine...
A ring R is called right strong stably finite (r.ssf) if for all n ≥ 1, injective endomorphisms of R (n) R are essential. If R is an r.ssf ring and e is an idempotent of R such that eR is a retractable R-module, then eRe is an r.ssf ring. A direct product of rings is an r.ssf ring if and only if each factor is so. The R.ssf condition is investigated for formal triangular matrix rings. In partic...
let r be a right gf-closed ring with finite left and right gorenstein global dimension. we prove that if i is an ideal of r such that r/i is a semi-simple ring, then the gorensntein flat dimensnion of r/i as a right r-module and the gorensntein injective dimensnnion of r/i as a left r-module are identical. in particular, we show that for a simple module s over a commutative gorensntein ring r, ...
Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on it. We define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong S-domains. As an application, we give new characterizations of $star$-quasi-Pr"{u}fer domains and UM$t$ domains in terms of dimension inequal...
A module $M$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $M$ into $M$. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.
we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel, that is, every simple right $r$-module has a flat $b$-cover. we give some properties of such rings along with examples. we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...
a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.
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