Weak baer modules localized with respect to a torsion theory
نویسندگان
چکیده
منابع مشابه
LIFTING MODULES WITH RESPECT TO A PRERADICAL
Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplusN_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting moduleis $tau_M$-lifting.
متن کاملRanks of modules relative to a torsion theory
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...
متن کاملranks of modules relative to a torsion theory
relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...
متن کامل–supplemented Modules Relative to a Torsion Theory
Let R be ring and M a right R-module. This article introduces the concept of τ −⊕-supplemented modules as follows: Given a hereditary torsion theory in Mod-R with associated torsion functor τ we say that a module M is τ −⊕-supplemented when for every submodule N of M there exists a direct summand K of M such that M = N +K and N ∩K is τ−torsion, and M is called completely τ −⊕-supplemented if ev...
متن کاملlifting modules with respect to a preradical
let $m$ be a right module over a ring $r$, $tau_m$ a preradical on $sigma[m]$, and$ninsigma[m]$. in this note we show that if $n_1, n_2in sigma[m]$ are two$tau_m$-lifting modules such that $n_i$ is $n_j$-projective ($i,j=1,2$), then $n=n_1oplusn_2$ is $tau_m$-lifting. we investigate when homomorphic image of a $tau_m$-lifting moduleis $tau_m$-lifting.
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1998
ISSN: 0011-4642,1572-9141
DOI: 10.1023/a:1022432031262