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Open AccessArticle

Constructing Some Logical Algebras with Hoops

1
Hatef Higher Education Institute, Zahedan 9816848165, Iran
2
Department of Mathematics, Jeju National University, Jeju 63243, Korea
3
Department of Mathematics, Shahid Beheshti University, Tehran 1983969411, Iran
4
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1243; https://doi.org/10.3390/math7121243
Received: 12 November 2019 / Revised: 12 December 2019 / Accepted: 13 December 2019 / Published: 16 December 2019
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
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. View Full-Text
Keywords: hoop; co-filter; Brouwerian semilattice; Heyting algebra; Wajsberg hoop; Hilbert algebra; BL-algebra hoop; co-filter; Brouwerian semilattice; Heyting algebra; Wajsberg hoop; Hilbert algebra; BL-algebra
MDPI and ACS Style

Kologani, M.A.; Song, S.-Z.; Borzooei, R.A.; Jun, Y.B. Constructing Some Logical Algebras with Hoops. Mathematics 2019, 7, 1243.

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