TY  - JOUR
T1  - Simple-separable modules
AU  - Trıbak, Rachid
AU  - Ech-chaouy, Rachid
PY  - 2024
DA  - July
DO  - 10.24330/ieja.1449459
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 29
EP  - 50
VL  - 36
IS  - 36
LA  - en
AB  - A module $M$ over a ring is called simple-separable if every simple submodule of $M$ is contained in a finitely generateddirect summand of $M$. While a direct sum of any family of simple-separable modules is shown to be always simple-separable, we prove thata direct summand of a simple-separable module does not inherit the property, in general. It is also shown that an injective module $M$over a right noetherian ring is simple-separable if and only if $M=M_1 \oplus M_2$ such that $M_1$ is separable and $M_2$ has zero socle.The structure of simple-separable abelian groups is completely described.
KW  - Separable module
KW  - simple-separable module
KW  - V-ring
KW  - $\pi$-V-ring
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UR  - https://doi.org/10.24330/ieja.1449459
L1  - https://dergipark.org.tr/en/download/article-file/3782093
ER  -