QUASI-VALUATION MAPS ON JU-ALGEBRAS INDUCED BY FILTERS

Abstract

The subject of this report is the observation of the concept of JU-filters in JU-algebras, which are a generalization of KU-algebras. In such algebras, the concept of quasi-valuation maps based on the ideal in them has already been developed. Additionally, the design of a quasi-metric space on a JU-algebra induced by that quasi-valuation map is considered. In this paper, the concept of quasi-valuation maps on JU-algebras based on a filter was designed. Then, some of its fundamental properties are shown. In addition, the concepts of quasi-valuation maps on JU-algebra based on implicative and comparative filters were constructed and analyzed. The interconnections of these three types of quasi-valuation maps on JU-algebras are also registered.