Affiliations: [a] Shahid Chamran Faculty, Technical and Vocational University, Kerman, Iran | [b] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Correspondence:
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Corresponding author. Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +98 34 31322490; E-mail: arsham@uk.ac.ir.
Abstract: In this paper, we first introduce the notion of Stonean implicative filter in Hilbert algebra and study it in detail. Finally, we introduce a Stonean Hilbert algebra and investigate its properties, we prove that, H is a Stonean Hilbert algebra if and only if the set of all regular elements of H is a Stonean Hilbert algebra. By the diagrams, we summarize the results of this paper and give the relationships between all types of filters in a Hilbert algebra. Also, we give the relationships between Hilbert algebra and some of algebraic structures.
