Results on Hyper Hoop-Algebras
R. A. Borzooei, Hamid Reza Varasteh, Keivan Borna, Akefe Radfar · New Mathematics and Natural Computation · 2017
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) [Formula: see text]-algebras, hyper [Formula: see text]-algebras, hyper [Formula: see text]-algebras, hyper [Formula: see text]-algebras and hyper [Formula: see text]-algebras.