Imploring GE-Filters of GE-Algebras

Abstract

Relations between a transitive GE-algebra, a belligerent GE-algebra, an antisymmetric GE-algebra, and a left exchangeable GE-algebra are displayed. A new substructure, so called imploring GE-filter, is introduced, and its properties are investigated. The relationship between a GE-filter, an imploring GE-filter, a belligerent GE-filter, and a prominent GE-filter are considered. Conditions for an imploring GE-filter to be a belligerent GE-filter are given, and the conditions necessary for a (belligerent) GE-filter to be an imploring GE-filter are found. Relations between a prominent GE-filter and an imploring GE-filter are discussed, and a condition for an imploring GE-filter to be a prominent GE-filter is provided. Examples to show that a belligerent GE-filter and a prominent GE-filer are independent concepts are given. The extension property of the imploring GE-filter is established.