TY - JOUR ID - 230 TI - ZARISKI-LIKE SPACES OF CERTAIN MODULES JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Fazaeli Moghim, H. AU - Rashedi, F. AD - Department of Mathematics, Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran. AD - Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran. Y1 - 2014 PY - 2014 VL - 1 IS - 2 SP - 101 EP - 115 KW - RSP module KW - Multiplication module KW - Zariski-like space KW - Subtractive subsemi- module KW - Subtractive basis DO - 10.22044/jas.2014.230 N2 - Let $R$ 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. UR - https://jas.shahroodut.ac.ir/article_230.html L1 - https://jas.shahroodut.ac.ir/article_230_b7b37843a5fe23f4743e67cb83ccec30.pdf ER -