Results on Hyper Hoop-Algebras

R. A. Borzooei, H. R. Varasteh (), K. Borna () and A. Radfar ()
Additional contact information
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

New Mathematics and Natural Computation (NMNC), 2017, vol. 13, issue 01, 61-74

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.

Keywords: (Hyper) Hoop-algebra; hyper BE-algebra; (hyper) BCK-algebra; hyper MV-algebra; hyper K-algebra; hyper I-algebra (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S1793005717500065

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