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Constructing Some Logical Algebras with Hoopsopen access
- Issue Date
- Dec-2019
- Publisher
- MDPI
- Keywords
- hoop; co-filter; Brouwerian semilattice; Heyting algebra; Wajsberg hoop; Hilbert algebra; BL-algebra
- Citation
- MATHEMATICS, v.7, no.12
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATICS
- Volume
- 7
- Number
- 12
- ISSN
- 2227-7390
- Abstract
- 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.
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