Pseudo-hoops

Abstract

In this paper we study the pseudo-hoops, structures introduced by B. Bosbach in [6,7] under the name of complementary semigroups. We prove some of their properties and we define the basic concepts of filter and normal filter. The lattice of normal filters is isomorphic with the lattice of congruences of a pseudo-hoop. We also study some important classes of pseudo-hoops. Bounded Wajsberg pseudo-hoops are equivalent to pseudo-Wajsberg algebras and bounded basic pseudo-hoops are equivalent to pseudo-BL algebras. Some examples of pseudo-hoops are given in the last section of the paper. © 2005 Old City Publishing, Inc.