Multiplication modules with prime spectrum
Authors : Ortaç Öneş, Mustafa Alkan
Pages : 2000-2009
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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