Extended Filters of MS -Algebras

Abstract

For a filter T of an MS -algebra L and a subset Z of L, a new extension filter of T is introduced, denoted by ET(Z). Many properties of ET(Z) are investigated and the lattice structure of the set of all ET(Z) is studied. A new definition related to ET(Z) is presented, called fixed filters relative to a subset of L. A generalisation of ET(Z) is illustrated by introducing the concept of strong filters, notated by ET(Z)¯¯¯¯¯¯¯¯¯¯¯¯¯¯. The strong extension ET(Z)¯¯¯¯¯¯¯¯¯¯¯¯¯¯ is characterized by the intersection of all strong filters fixed relative to an ideal L−P for a prime filter P of L.