L-fuzzy prime spectra of ordered semigroups

Article type: Research Article

Authors: Wu, Huanrong | Yu, Bin^{; *}

Affiliations: College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China

Correspondence: [*] Corresponding author. Bin Yu, College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China. E-mail: [email protected].

Abstract: The aim of this paper is to develop the spectral theory of prime L-ideals in ordered semigroups. Firstly the concepts of an L-fuzzy ideal and that of an L-fuzzy prime ideal are given and discussed. And then a topological space, called the L-fuzzy prime spectrum of an ordered semigroup, has been gained. This topological space is T1 and sober. Furthermore some homeomorphic spaces of this topological space are investigated. Finally, a contravariant functor from the category of commutative ordered semigroups into the category of sober topological spaces is obtained.

Keywords: Ordered semigroup, prime L-fuzzy ideal, spectrum, contravariant functor

DOI: 10.3233/JIFS-18743

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 3, pp. 3847-3857, 2018