A representation for radicals in pseudo BL-algebras

Article type: Research Article

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

Affiliations: [a] Department of Mathematics, Payame Noor University, Tehran, Iran | [b] Mahani Mathematical Research center, Shahid Bahonar University of Kerman, Kerman, Iran | [c] 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 and Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +3431322490; E-mail: [email protected].

Abstract: In this paper, we intend to introduce the notion of the radical of a filter in a pseudo BL-algebra and express its characteristics and properties. We define dense, infinitesimal, nilpotent, and unity elements in a pseudo BL-algebra, and then, investigate the relationship between these elements and the radical in a pseudo BL-algebra. Our study revealed significant results in this regard.

Keywords: Pseudo BL-algebra, (Prime, Maximal) filter, Radical, (Dense, Infinitesimal, Nilpotent, Unity) element

DOI: 10.3233/JIFS-181039

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 2, pp. 1443-1454, 2019