On maximal filters in triangle algebras

Article type: Research Article

Authors: Zahiri, Saeide | Borumand Saeid, Arsham^* | Eslami, Esfandiar

Affiliations: Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Correspondence: [*] Corresponding author. Dr. Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +98 34 31322490; Fax: +98 34 33201080; E-mail: [email protected].

Abstract: In this paper, we define two types of maximal filters in triangle algebras. The concepts of the radical of a triangle algebra and radical of an interval valued residuated lattice-filter (IVRL-filter) in triangle algebras are introduced. Some characterizations of the radical of an IVRL-filter are given. The notion of IVRL-extended semi maximal filter in triangle algebras also introduced. We investigate the relations between this notion and other types of IVRL-filters in triangle algebras. Special elements such as dense elements and double complemented elements in triangle algebras are defined. Properties of the collections of these elements as well as properties of IVRL-filters in triangle algebras are studies.

Keywords: Triangle algebra, IVRL-filter, maximal, radical, dense element, double complemented element

DOI: 10.3233/IFS-151842

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1181-1193, 2016