ZARISKI-LIKE SPACES OF CERTAIN MODULES

Let R be a commutative ring with identity and M be a unitary R-module. The primary-like spectrum SpecL(M) is the collection of all primary-like submodules Q such that M/Q is a primeful R-module. Here, M is de ned to be RSP if rad(Q) is a prime submodule for all Q € SpecL(M). This class contains the family of multiplication modules properly. The purpose of this paper is to introduce and investigates a new Zariski space of an RSP module, called a Zariski-like space. In particular, we provide conditions under which the Zariski-like space of a multiplication module has a subtractive basis.

Keywords:

RSP module , Multiplication module , Zariski-like space , Subtractive subsemi-module , Subtractive basis