TY - JOUR
ID - 416
TI - On H-cofinitely supplemented modules
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Talebi, Y.
AU - Tribak, R.
AU - Moniri Hamzekolaei, A. R.
AD - University of Mazandaran, Iran
AD - University of Tetouan
AD - Univeristy of Mazandaran, Iran
Y1 - 2013
PY - 2013
VL - 39
IS - 2
SP - 325
EP - 346
KW - H-supplemented module
KW - H-cofinitely supplemented module
KW - radical-projective module
DO -
N2 - A module $M$ is called $emph{H}$-cofinitely supplemented if for every cofinite submodule $E$ (i.e. $M/E$ is finitely generated) of $M$ there exists a direct summand $D$ of $M$ such that $M = E + X$ holds if and only if $M = D + X$, for every submodule $X$ of $M$. In this paper we study factors, direct summands and direct sums of $emph{H}$-cofinitely supplemented modules. Let $M$ be an $emph{H}$-cofinitely supplemented module and let $N leq M$ be a submodule. Suppose that for every direct summand $K$ of $M$, $(N + K)/N$ lies above a direct summand of $M/N$. Then $M/N$ is $emph{H}$-cofinitely supplemented. Let $M$ be an $emph{H}$-cofinitely supplemented module. Let $N$ be a direct summand of $M$. Suppose that for every direct summand $K$ of $M$ with $M=N+K$, $Ncap K$ is also a direct summand of $M$. Then $N$ is $emph{H}$-cofinitely supplemented. Let $M = M_{1} oplus M_{2}$. If $M_{1}$ is radical $M_{2}$-projective (or $M_{2}$ is radical $M_{1}$-projective) and $M_{1}$ and $M_{2}$ are $emph{H}$-cofinitely supplemented, then $M$ is $emph{H}$-cofinitely supplemented
UR - http://bims.iranjournals.ir/article_416.html
L1 - http://bims.iranjournals.ir/article_416_a39509657a78fc90c5d27db44e1ed1d3.pdf
ER -