# $\oplus $-cofinitely supplemented modules

Czechoslovak Mathematical Journal (2004)

- Volume: 54, Issue: 4, page 1083-1088
- ISSN: 0011-4642

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topÇalışıcı, 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 -

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