Classification of some elements in pseudo BL-algebras

Article type: Research Article

Authors: Daneshpayeh, Roohallah^a | Borumand Saeid, Arsham^{b; *} | Mirvakili, Saeed^a | Rezaei, Akbar^a

Affiliations: [a] Department of Mathematics, Payame Noor University, Tehran, Iran | [b] Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran; Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Correspondence: [*] Corresponding author. Arsham Borumand Saeid, Mahani Mathematical Research center, Shahid Bahonar University of Kerman, Kerman, Iran. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.+98 34 31322490; E-mail: [email protected].

Abstract: In this paper, the notions of orthogonal, dense, regular, zero-divisor, strong and complemented elements in a pseudo BL-algebra are introduced and relation between the orthogonal and zero-divisor elements for perfect (good) pseudo BL-algebras is investigated. In particular, we get some results when a pseudo BL- algebra is good or perfect. Finally, a new characterization of these elements in a pseudo BL-algebra by a diagram is given.

Keywords: Pseudo BL-algebra, (Perfect, Primary) filter, radical, (Orthogonal, Dense, Regular, Zero divisor, Strong, Complemented) elements

DOI: 10.3233/JIFS-181218

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 6, pp. 6367-6377, 2018