SOME TYPES OF FILTERS IN EQUALITY ALGEBRAS

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BORZOOEI R.A.; ZEBARDAST F.; AALY KOLOGANI M.

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Journal: Categories and General Algebraic Structures with Applications Year:2017 | Volume:7 | Issue:SUPP. Page(s): 33-55

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Title

SOME TYPES OF FILTERS IN EQUALITY ALGEBRAS

Author(s)

BORZOOEI R.A. | ZEBARDAST F. | AALY KOLOGANI M. | Issue Writer Certificate

Keywords

EQUALITY ALGEBRAQ4

(POSITIVE) IMPLICATIVE FILTERQ4

FANTASTIC FILTERQ4

BOOLEAN FILTERQ4

Abstract

EQUALITY ALGEBRAs were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in EQUALITY ALGEBRAs and we prove some results which determine the relation between these filters. We prove that the quotient EQUALITY ALGEBRA induced by an implicative filter is a Boolean algebra, by a FANTASTIC FILTER is a commutative EQUALITY ALGEBRA, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and BOOLEAN FILTERs are equivalent on bounded commutative EQUALITY ALGEBRAs.

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APA: Copy

BORZOOEI, R.A., ZEBARDAST, F., & AALY KOLOGANI, M.. (2017). SOME TYPES OF FILTERS IN EQUALITY ALGEBRAS. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 7(SUPP.), 33-55. SID. https://sid.ir/paper/255410/en

Vancouver: Copy

BORZOOEI R.A., ZEBARDAST F., AALY KOLOGANI M.. SOME TYPES OF FILTERS IN EQUALITY ALGEBRAS. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2017;7(SUPP.):33-55. Available from: https://sid.ir/paper/255410/en

IEEE: Copy

R.A. BORZOOEI, F. ZEBARDAST, and M. AALY KOLOGANI, “SOME TYPES OF FILTERS IN EQUALITY ALGEBRAS,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 7, no. SUPP., pp. 33–55, 2017, [Online]. Available: https://sid.ir/paper/255410/en

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