Constructing Some Logical Algebras with Hoops

M. Aaly Kologani, Seok-Zun Song, R. A. Borzooei and Young Bae Jun
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M. Aaly Kologani: Hatef Higher Education Institute, Zahedan 9816848165, Iran
Seok-Zun Song: Department of Mathematics, Jeju National University, Jeju 63243, Korea
R. A. Borzooei: Department of Mathematics, Shahid Beheshti University, Tehran 1983969411, Iran
Young Bae Jun: Department of Mathematics, Shahid Beheshti University, Tehran 1983969411, Iran

Mathematics, 2019, vol. 7, issue 12, 1-13

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.

Keywords: hoop; co-filter; Brouwerian semilattice; Heyting algebra; Wajsberg hoop; Hilbert algebra; BL-algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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