ZARISKI-LIKE SPACES OF CERTAIN MODULES

Let r be a commutative ring with identity and mbe a unitary r-module. the primary-like spectrum specl(m) isthe collection of all primary-like submodules q such that m=q isa primeful r-module. here, m is dened to be rsp if rad(q)is a prime submodule for all q 2 specl(m). this class containsthe family of multiplication modules properly. the purpose of thispaper is to introduce and investigates a new zariski space of anrsp module, called a zariski-like space. in particular, we provideconditions under which the zariski-like space of a multiplicationmodule has a subtractive basis.