Geodesic
A homological approach to $\oplus$-supplemented modules
Novi Sad Journal of Mathematics, Tome 50 (2020) no. 2.

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$\oplus$-supplemented modules as a famous generalization of lifting (projective supplemented) modules were widely studied in the last decades. In this paper, we peruse a homological approach to $\oplus$-supplemented modules. Let $R$ be a ring, $M$ a right $R$-module and $S=End_{R}(M)$. We say that $M$ is endomorphism $\oplus$-supplemented (briefly, $E$-$\oplus$-supplemented) provided that for every $f\in S$, there exists a direct summand $D$ of $M$ such that $Imf+D=M$ and $Imf\cap D\ll D$. We investigate some general properties of $E$-$\oplus$-supplemented modules and try to consider their relation with some known classes of modules such as dual Rickart modules, $H$-supplemented modules and $\oplus$-supplemented modules.
Publié le :
DOI : 10.30755/NSJOM.10240
Classification : 16D10, 16D40, 16D80
Keywords: $\oplus$-supplemented module, $E$-$H$-supplemented module, dual Rick art module, $E$-$\oplus$-supplemented module, small submodule 
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     author = {Sepideh Khajvand Sany and Ali Reza Moniri Hamzekolaee and Yahya Talebi},
     title = {A homological approach to $\oplus$-supplemented modules},
     journal = {Novi Sad Journal of Mathematics},
     pages = {131 - 142},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2020},
     doi = {10.30755/NSJOM.10240},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.10240/}
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Sepideh Khajvand Sany; Ali Reza Moniri Hamzekolaee; Yahya Talebi. A homological approach to $\oplus$-supplemented modules. Novi Sad Journal of Mathematics, Tome 50 (2020) no. 2. doi : 10.30755/NSJOM.10240. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.10240/

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