Shahrood University of TechnologyJournal of Algebraic Systems2345-51281220140101ZARISKI-LIKE SPACES OF CERTAIN MODULES10111523010.22044/jas.2014.230ENH.Fazaeli MoghimDepartment of Mathematics, Department of Mathematics, University of Birjand,
P.O. Box 97175-615, Birjand, Iran.F.RashediDepartment of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand,
Iran.Journal Article20130413Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The primary-like spectrum $Spec_L(M)$ is the collection of all primary-like submodules $Q$ such that $M/Q$ is a primeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ is a prime submodule for all $Q\in Spec_L(M)$. This class contains the family of multiplication modules properly. The purpose of this paper is to introduce and investigate a new Zariski space of an RSP module, called Zariski-like space. In particular, we provide conditions under which the Zariski-like space of a multiplication module has a subtractive basis.https://jas.shahroodut.ac.ir/article_230_b7b37843a5fe23f4743e67cb83ccec30.pdf