%0 Journal Article %T Results on hoops %J Journal of Algebraic Hyperstructures and Logical Algebras %I University of Hatef (Hatef College University) %Z 2676-6000 %A Borzooei, R.A. %A Aaly, M. %D 2020 %\ 02/01/2020 %V 1 %N 1 %P 61-77 %! Results on hoops %K Hoop %K residuated lattice %K Equality algebra %K EQ-algebra %K Hilbert algebra %R 10.29252/hatef.jahla.1.1.5 %X In this paper, by considering the notion of hoop, were introduced by Bosbach in [7, 8] under the name of complementary semigroups, we show that there are relations among hoops and some of other logical algebras such as residuated lattices, MT L-algebras, BL-algebras, MV-algebras, BCK-algebras, equality algebras, EQ-algebras, R0-algebras, Hilbert algebras, Heyting algebras, Hertz algebras, lattice implication algebras and fuzzy implication algebras. The aim of this paper is to find that under what conditions hoops are equivalent to these logical algebras. %U https://jahla.hatef.ac.ir/article_101797_fef2c5457779c4d7044b00bfcd9d0e61.pdf