Turkish Journal of Mathematics
Article Title
Multiplication modules with prime spectrum
DOI
10.3906/mat-1803-54
Abstract
The subject of this paper is the Zariski topology on a multiplication module $M$ over a commutative ring $R$. We find a characterization for the radical submodule $rad_{M}(0)$ and also show that there are proper ideals $I_{1},...,I_{n}$ of $R$ such that $rad_{M}(0)=rad_{M}(\left( I_{1}...I_{n}\right) M)$. Finally, we prove that the spectrum $Spec(M)$ is irreducible if and only if $M$ is the finite sum of its submodules, whose $ \mathcal{T}$-radicals are prime in $M$.
Keywords
Multiplication module, prime submodule, spectrum of module
First Page
2000
Last Page
2009
Recommended Citation
ÖNEŞ, ORTAÇ and ALKAN, MUSTAFA
(2019)
"Multiplication modules with prime spectrum,"
Turkish Journal of Mathematics: Vol. 43:
No.
4, Article 15.
https://doi.org/10.3906/mat-1803-54
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss4/15
