Investigating Pre A* Algebras as an Emerging Paradigm

Abstract

This paper explores Boolean algebra postulate systems, aiming to derive a minimal set of axioms. It delves into the algebraic structure of Pre A*-algebras and establishes the congruence relation on them. Defining a ternary operation as a conditional statement, the paper explores its properties. Pre A* algebras are obtained from Boolean Algebra B, and it is proven that if A is a Pre A*-algebra and x is in A, then Ax is a Pre A*-algebra, isomorphic to a quotient algebra of A.