ZARISKI-LIKE SPACES OF CERTAIN MODULES

Document Type : Original Manuscript

Authors

1 Department of Mathematics, Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran.

2 Department of Mathematics, University of Birjand, P.O. Box 97175-615, Birjand, Iran.

Abstract

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 defined 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 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.

Keywords

Journal of Algebraic Systems
Volume 1, Issue 2 - Serial Number 2
January 2014
Pages 101-115

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