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Results on Hyper Hoop-Algebras

Author

Listed:
  • R. A. Borzooei

    (Department of Mathematics, Shahid Beheshti University, Tehran, Iran)

  • H. R. Varasteh

    (#x2020;Research and Technology Office, Kharazmi University, Tehran, Iran)

  • K. Borna

    (#x2021;Faculty of Mathematics and Computer Science, Kharazmi University, Tehran, Iran)

  • A. Radfar

    (#xA7;Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran)

Abstract

Hoop-algebra is a naturally ordered commutative residuated integral monoids, which is introduced by B. Bosbach in Refs. 7 and 8. Now, in this paper, by considering the notion of hyper hoop-algebra, we find a condition to obtain a hoop from a finite bounded hyper hoop-algebra. Then we investigate the relations among hyper hoop-algebras and some of the other logical (hyper) algebras such as (hyper) BCK-algebras, hyper K-algebras, hyper BE-algebras, hyper I-algebras and hyper MV-algebras.

Suggested Citation

  • R. A. Borzooei & H. R. Varasteh & K. Borna & A. Radfar, 2017. "Results on Hyper Hoop-Algebras," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 61-74, March.
    • Handle: RePEc:wsi:nmncxx:v:13:y:2017:i:01:n:s1793005717500065
    DOI: 10.1142/S1793005717500065
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