RELATIVE TORSION
نویسندگان
چکیده
منابع مشابه
A relative extending module and torsion precovers
We first characterize $tau$-complemented modules with relative (pre)-covers. We also introduce an extending module relative to $tau$-pure submodules on a hereditary torsion theory $tau$ and give its relationship with $tau$-complemented modules.
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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 کاملa relative extending module and torsion precovers
we first characterize $tau$-complemented modules with relative (pre)-covers. we also introduce an extending module relative to $tau$-pure submodules on a hereditary torsion theory $tau$ and give its relationship with $tau$-complemented modules.
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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...
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This paper achieves, among other things, the following: • It frees the main result of [BFKM] from the hypothesis of determinant class and extends this result from unitary to arbitrary representations. • It extends (and at the same times provides a new proof of) the main result of Bismut and Zhang [BZ] from finite dimensional representations of Γ to representations on an A−Hilbert module of fini...
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ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2001
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199701000287