WEAK FILTERS AND MULTIPLIERS IN SHEFFER STROKE HILBERT ALGEBRAS

Abstract

With the aim of discussing the weak filters and multipliers of the Sheffer stroke Hilbert algebra, the concept of weak filters that weakened the filter conditions in the Sheffer stroke Hilbert algebra is first introduced and their properties are investigated. A method of making a weak filter using the notion of ideals is presented, and the shape of the weak filter is investigated in the Cartesian product of the Sheffer stroke Hilbert algebra. Second, the concept of multipliers in Sheffer stroke Hilbert algebras is introduced, and the various properties involved are examined. The image and pre-image of weak filters by multipliers are discussed. The kernel and a fixed set of multipliers are found to be weak filters. The composition of multipliers is studied, and the conditions under which the two multipliers are equal are explored. The conditions under which the two multipliers are equal are explored. By assigning a Sheffer stroke to the set of multipliers, a new Sheffer stroke Hilbert algebra is derived. © Palestine Polytechnic University-PPU 2025.