%0 Journal Article
%T Ranks of modules relative to a torsion theory
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Asgari, Sh.
%A Haghany, A.
%D 2011
%\ 12/15/2011
%V 37
%N No. 4
%P 19-33
%! Ranks of modules relative to a torsion theory
%K Hereditary torsion theory
%K pseudo $tau$-essential
%K pseudo
$tau$-uniform
%K $tau$-rank
%R
%X 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.
%U http://bims.iranjournals.ir/article_368_1af8f9a81692bba1f4aa0fc6001c47b7.pdf