On the Zariski topology over an $L$-module $M$ | Zendy

Fethi Çallıalp | Zendy; Gülşen Ulucak | Zendy; Ünsal Teki̇̀r | Zendy

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On the Zariski topology over an $L$-module $M$

Author(s) -

Fethi Çallıalp,

Gülşen Ulucak,

Ünsal Teki̇̀r

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1502-31

Subject(s) - mathematics , multiplicative function , topology (electrical circuits) , prime (order theory) , sigma , lattice (music) , product topology , general topology , initial topology , topological space , extension topology , discrete mathematics , combinatorics , mathematical analysis , physics , quantum mechanics , acoustics

Let L be a multiplicative lattice and M be an L -module. In this study, we present a topology said to be the Zariski topology over σ(M), the collection of all prime elements of an L -module M. We research some results on the Zariski topology over σ(M). We show that the topology is a T0 -space and a T1 -space under some conditions. Some properties and results are studied for the topology over σ(L) , the collection of all prime elements of a multiplicative lattice L.

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