IRREDUCIBLE GE-FILTERS AND GE-MORPHISMS IN GE-ALGEBRAS

Abstract

The concepts of irreducible GE-filter and under-system are introduced and their properties are investigated in a GE-algebra. Given a GE-filter, the existence of irreducible GE-filter containing it is revealed.Conditions for a GE-filter to be irreducible are given. The irreducible GE-filter is used to characterize weak GE-morphism. The existence of irreducible GE-filter which contains a GE-filter and is disjoint with an under-system is established. Based on GE-morphism, the existence of irreducible GE-filter is discussed. Conditions that allow a weak GE-morphism to be a GE-morphism are explored, and a necessary and sufficient condition for a GE-morphism to be injective is given. © Palestine Polytechnic University-PPU 2024.