On Anti-Regular Ternary Algebras

Abstract

A ternary algebra is an algebraic system consisting of a nonempty set together with two different ternary algebraic operations, called “additive ternary” and “multiplicative ternary”.  The notions of anti- additive regular ternary algebras and  anti- multiplicative regular ternary algebras are defined.  Some properties of  anti- additive regular ternary algebras and  anti- multiplicative regular ternary algebras are given. Moreover, we define the notions of anti-additive and anti - multiplicative equivalence relations  on  ternary algebras. Furthermore, we introduce the notion of quotient ternary algebras by using anti-additive and anti-multiplicative regular equivalence relations.