Constructing Some Logical Algebras with Hoops

In any logical algebraic structures, by using of different kinds of filters, one can construct various kinds of other logical algebraic structures. With this inspirations, in this paper by considering a hoop algebra or a hoop, that is introduced by Bosbach, the notion of co-filter on hoops is introd...

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Bibliographic Details
Published inMathematics (Basel) Vol. 7; no. 12; p. 1243
Main Authors Kologani, M. Aaly, Song, Seok-Zun, Borzooei, R. A., Jun, Young Bae
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2019
Subjects
Algebra
Food science
Hoops
Quotients
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Summary:In any logical algebraic structures, by using of different kinds of filters, one can construct various kinds of other logical algebraic structures. With this inspirations, in this paper by considering a hoop algebra or a hoop, that is introduced by Bosbach, the notion of co-filter on hoops is introduced and related properties are investigated. Then by using of co-filter, a congruence relation on hoops is defined, and the associated quotient structure is studied. Thus Brouwerian semilattices, Heyting algebras, Wajsberg hoops, Hilbert algebras and BL-algebras are obtained.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7121243