ranks of modules relative to a torsion theory

Authors

sh. asgari

a. haghany

abstract

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 complements to $tau$-torsionfree submodules of $m$ are obtained.

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Journal title:
bulletin of the iranian mathematical society

Publisher: iranian mathematical society (ims)

ISSN 1017-060X

volume 37

issue No. 4 2011

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