TY  - JOUR
T1  - Quasi-primry submodules satisfying the primeful property I
AU  - Moghimi, Hosein Fazaeli
AU  - Samiei, Mahdi
PY  - 2016
DA  - October
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1421
EP  - 1434
VL  - 45
IS  - 5
LA  - en
AB  - Let $R$ be a commutative ring with identity and $M$a unital$R$-module. In this article we extend the notion of quasi-primary ideals to submodules. A proper submodule $N$ of $M$ is called quasi-primary if whenever $rx\in N$ for $r\in R$ and $x\in M$, then $r\in \sqrt{(N:M)}$ or $x\in radN$ where $radN$ is the intersection of all prime submodules of $M$ containing $N$. Also, we say that a submodule $N$ of $M$satisfies the primeful property if $M/N$ is a primeful$R$-module. For a quasi-primary submodule $N$ of $M$ satisfying the primeful property,$\sqrt{(N:M)}$ is a prime ideal of $R$. For the existence of a module-reduced quasi-primary decomposition, the radical of each term appeared in decomposition must be prime. We provide sufficient conditions, involving the saturation and torsion arguments, to ensure that this property holds as is valid in the ideal case. It is proved that for a submodule $N$ of $M$ over a Dedekind domain $R$ which satisffies the primeful property, $N$ is quasi-primary if and only if $radN is prime.
KW  - Quasi-primary submodule
KW  - Primeful property
KW  - Prime submodule
KW  - Radical of a submodule
KW  - Saturation
KW  - Torsion
CR  - .
CR  - .
UR  - https://dergipark.org.tr/en/pub/hujms/issue//524332
L1  - https://dergipark.org.tr/en/download/article-file/644708
ER  -