On algebras of distributions of isolating formulas of theory of abelian groups and their ordered enrichings

We describe algebras of distributions of binary isolating formulas for theories of abelian groups and their ordered enriching. This description is based on general theory of algebras of isolating formulas and uses the specificity of basedness of theories of abelian groups which is based on Shmeleva's invariants. We give Cayley tables for algebras corresponding to theories of base abelian groups and their ordered enrichings, and point out a machinery of transformation of theories of base abelian groups into algebras for arbitrary theories of abelian groups.