Multiplication modules with prime spectrum

Authors

ORTAÇ ÖNEŞ
MUSTAFA ALKAN

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 $M$.

DOI

10.3906/mat-1803-54

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