Zariski topology over multiplication Krasner hypermodules

Abstract

UDC 512.5 In this paper, we introduce the notion of multiplication Krasner hypermodules over commutative hyperrings and topologize the collection of all multiplication Кrasner hypermodules. In addition, we investigate some properties of this topological space.

The Spectrum of the Zariski Topology for Multiplication Krasner Hypermodules

“…Recall from [17] that a hypermodule N is called multiplication S-hypermodule if for each subhypermodule K of N, there is a hyperideal J of S so that K = [J.N].…”

“…We use denoting N as a topological S-hypermodule in the rest of this text. In [17], we investigate the Zariski topology over multiplication hypermodules. Zariski topology is built on topological modules in [14].…”

“…

In this study, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings in [17]. Firstly we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hyper-modules, then we give some relevant properties of the hypermodule in this topological hyperspace.

…”

Spectrum of Zariski Topology in Multiplication Krasner Hypermodules

“…Recall from [11] that a hypermodule N is multiplication S-hypermodule if, for each subhypermodule K of N, there exists a hyperideal J of S with K =…”

“…Hypergroup theory, which was defined in [1] as a more comprehensive algebraic structure of group theory, has been investigated by different authors in modern algebra. It has been developed using hyperring and hypermodule theory studies by many authors in a series of papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Following these papers, let us start by giving the basic information necessary for the algebraic structure that we will study as Krasner S-hypermodule in studying the S-hypermodule class on a fixed Krasner hyperring class S. Let N be a nonempty set; (N, •) is called a hypergroupoid if for the map defined as • : N × N −→ P * (N) is a function.…”