Ideals of S-Algebra and Hull Kernel Topology on Idealistic S-Algebra

Abstract

An S-algebra is an algebra of type (2, 2) that provides a common generalization of several algebraic structures, including distributive lattices, Boolean algebras, and C-algebras. In this paper we study the ideals of an S-algebra. We describe the ideal generated by a nonempty subset, prove that the ideals of an S-algebra form a complete lattice under inclusion, and determine the principal ideals. We then introduce the notion of an Idealistic S-algebra and establish several equivalent characterizations of its prime ideals. Finally, we equip the set of prime ideals of an Idealistic S-algebra with the hull–kernel topology and study its basic properties.