TY - JOUR
ID - 368
TI - Ranks of modules relative to a torsion theory
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Asgari, Sh.
AU - Haghany, A.
AD -
Y1 - 2011
PY - 2011
VL - 37
IS - No. 4
SP - 19
EP - 33
KW - Hereditary torsion theory
KW - pseudo $tau$-essential
KW - pseudo
$tau$-uniform
KW - $tau$-rank
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_368.html
L1 - http://bims.iranjournals.ir/article_368_1af8f9a81692bba1f4aa0fc6001c47b7.pdf
ER -