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Constructing Some Logical Algebras with Hoops

Author

Listed:
  • 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
    Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea)

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.

Suggested Citation

  • M. Aaly Kologani & Seok-Zun Song & R. A. Borzooei & Young Bae Jun, 2019. "Constructing Some Logical Algebras with Hoops," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1243-:d:298376
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