Semi maximal filter in Hilbert algebra

Article type: Research Article

Authors: Soleimani Nasab, Ali¹ | Borumand Saeid, Arsham^*

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

Correspondence: [*] Correspondence author: Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +98 34 31322490; Fax: +98 34 33201080; E-mail: arsham@uk.ac.ir.

Note: [1] Permanent address: Shahid Chamran Faculty, Technical and Vocational University, Kerman, Iran. E-mail: asoleimaninasab@gmail.com.

Abstract: In this paper, the radical of an implicative filter in Hilbert algebras is studied and some theorems are given on its properties and we show that radical form a closure operator. Also, the radical of the set of all regular elements is characterized. Finally, the notion of semi maximal filter is introduced as a closed set of that closure operator and studied it in detail.

Keywords: (semisimple,local), Hilbert algebra (with supremum), radical of an implicative filter, semi maximal filter

DOI: 10.3233/IFS-151706

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 7-15, 2016