Prominent interior GE-filters of GE-algebras

Abstract

The concept of a prominent interior GE-filter (of type 1 and type 2) is introduced, and their properties are investigated. The relationship between a prominent GE-filter and a prominent interior GE-filter and the relationship between an interior GE-filter and a prominent interior GE-filter are discussed. Examples to show that any interior GE-filter is not a prominent interior GE-filter and any prominent GE-filter is not a prominent interior GE-filter are provided. Conditions for an interior GE-filter to be a prominent interior GE-filter are given. Also, conditions under which an internal GE filter larger than a given internal GE filter can become a prominent internal GE-filter are considered, and an example describing it is given. The relationship between a prominent interior GE-filter and a prominent interior GE-filter of type 1 is discussed.