$\oplus$-cofinitely supplemented modules

Çalışıcı, H., and Pancar, A.. "$\oplus $-cofinitely supplemented modules." Czechoslovak Mathematical Journal 54.4 (2004): 1083-1088. <http://eudml.org/doc/30923>.

@article{Çalışıcı2004,
abstract = {Let $R$ be a ring and $M$ a right $R$-module. $M$ is called $ \oplus $-cofinitely supplemented if every submodule $N$ of $M$ with $\frac\{M\}\{N\}$ finitely generated has a supplement that is a direct summand of $M$. In this paper various properties of the $\oplus $-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of $\oplus $-cofinitely supplemented modules is $\oplus $-cofinitely supplemented. (2) A ring $R$ is semiperfect if and only if every free $R$-module is $\oplus $-cofinitely supplemented. In addition, if $M$ has the summand sum property, then $M$ is $\oplus $-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of $M$.},
author = {Çalışıcı, H., Pancar, A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {cofinite submodule; $\oplus $-cofinitely supplemented module; cofinite submodules; cofinitely supplemented modules; summand sum property; direct summands; semiperfect rings},
language = {eng},
number = {4},
pages = {1083-1088},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$\oplus $-cofinitely supplemented modules},
url = {http://eudml.org/doc/30923},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Çalışıcı, H.
AU - Pancar, A.
TI - $\oplus $-cofinitely supplemented modules
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 4
SP - 1083
EP - 1088
AB - Let $R$ be a ring and $M$ a right $R$-module. $M$ is called $ \oplus $-cofinitely supplemented if every submodule $N$ of $M$ with $\frac{M}{N}$ finitely generated has a supplement that is a direct summand of $M$. In this paper various properties of the $\oplus $-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of $\oplus $-cofinitely supplemented modules is $\oplus $-cofinitely supplemented. (2) A ring $R$ is semiperfect if and only if every free $R$-module is $\oplus $-cofinitely supplemented. In addition, if $M$ has the summand sum property, then $M$ is $\oplus $-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of $M$.
LA - eng
KW - cofinite submodule; $\oplus $-cofinitely supplemented module; cofinite submodules; cofinitely supplemented modules; summand sum property; direct summands; semiperfect rings
UR - http://eudml.org/doc/30923
ER -