Integral hoops and integral filters

Abstract

In this paper, we introduced a new class of hoops, which are called integral hoops. In order to portray integral hoops, we introduced a new type of filters, named integral filters. We consider fundamental properties of integral hoops and integral filters and give some characterizations of them. Also, we discuss the relations between integral hoops and other types of hoops and prove that an integral hoop is a prefect and local hoop. Especially, we proved that every cancellative hoop is an integral hoop but the converse is not true. Finally, we discuss the relations between integral filters and some types of filters (obstinate, primary, prefect filters) in hoops and prove a filter F is an integral filter if and only if L/F is an integral hoop.