Results on hoops

In this paper, by considering the notion of hoop, were introduced byBosbach in [7, 8] under the name of complementary semigroups, weshow 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, latticeimplication algebras and fuzzy implication algebras. The aim of thispaper is to find that under what conditions hoops are equivalent tothese logical algebras.