Displaying similar documents to “On μ -singular and μ -extending modules”

On generalized q.f.d. modules

Mohammad Saleh, S. K. Jain, Sergio R. López-Permouth (2005)

Archivum Mathematicum

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A right R -module M is called a generalized q.f.d. module if every M-singular quotient has finitely generated socle. In this note we give several characterizations to this class of modules by means of weak injectivity, tightness, and weak tightness that generalizes the results in [sanh1], Theorem 3. In particular, it is shown that a module M is g.q.f.d. iff every direct sum of M -singular M -injective modules in σ [ M ] is weakly injective iff every direct sum of M -singular weakly tight is weakly...

Generalizations of coatomic modules

M. Koşan, Abdullah Harmanci (2005)

Open Mathematics

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For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ L≤ M| L is a δ-small submodule of M} = Re jm(℘)=∩{ N⊂ M: M/N∈℘. We call M δ-coatomic module whenever N≤ M and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module R R(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove...

On endomorphisms of multiplication and comultiplication modules

H. Ansari-Toroghy, F. Farshadifar (2008)

Archivum Mathematicum

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Let R be a ring with an identity (not necessarily commutative) and let M be a left R -module. This paper deals with multiplication and comultiplication left R -modules M having right End R ( M ) -module structures.

Injective and projective properties of R [ x ] -modules

Sangwon Park, Eunha Cho (2004)

Czechoslovak Mathematical Journal

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We study whether the projective and injective properties of left R -modules can be implied to the special kind of left R [ x ] -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.