Extension of stabilizers on subtraction algebras

This paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The study reveals that both the stabilizer of a subset and the stabilizer of an ideal with respect to another ideal are, in fact, ideals themselves. Investigating the impact of stabilizers on product and quotient subtraction algebras is a focal point. Additionally, a novel concept termed the ”stabilizer operation” is defined, and it is proven that the collection of ideals endowed with a binary stabilizer operator forms a bounded Hilbert algebra.