Turkish Journal of Mathematics
Abstract
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a quasi $J$-submodule if whenever $r\in R$ and $m\in M$ such that $rm\in N$ and $r\notin(J(R)M:M)$, then $m\in M$-$rad(N)$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Furthermore, we provide new classes of modules generalizing presimplifiable modules and justify their relation with (quasi) $J$-submodules. Finally, for a submodule $N$ of $M$ and an ideal $I$ of $R$, we characterize the quasi $J$-ideals of the idealization ring $R(+)M$.
DOI
10.55730/1300-0098.3290
Keywords
Quasi $J$-submodule, $J$-submodule, quasi $J$-ideal, quasi $J$-presimplifiable module, $J$-presimplifiable module
First Page
2610
Last Page
2624
Recommended Citation
ÇELİKEL, ECE YETKİN and KHASHAN, HANI
(2022)
"Quasi $J$-submodules,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 4.
https://doi.org/10.55730/1300-0098.3290
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/4
