@article {
author = {Asgari, Sh. and Haghany, A.},
title = {Ranks of modules relative to a torsion theory},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {37},
number = {No. 4},
pages = {19-33},
year = {2011},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
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.},
keywords = {Hereditary torsion theory,pseudo $tau$-essential,pseudo
$tau$-uniform,$tau$-rank},
url = {http://bims.iranjournals.ir/article_368.html},
eprint = {http://bims.iranjournals.ir/article_368_1af8f9a81692bba1f4aa0fc6001c47b7.pdf}
}