SPECIAL HOOP ALGEBRAS

Abstract

Hoops are naturally ordered commutative residuated integral monoids, introduced by B. Bosbach in [5,6].  In this paper, we introduce the concepts of special hoop algebra and special filter in hoop algebras and study some properties of them.  We establish relation between special hoops with other structures such as simple hoops, local hoops, locally finite hoops, perfect hoops, semi-De Morgan algebras and Boolean algebras.  Then, by define the notion of special filter in bounded hoops, we study the relationship between special filters and implicative (positive implicative, maximal, obstinate) filters on bounded and special hoops.  Finally, we investigated the properties of a quotient structure, when it is produced by a special filter.