On Anti-Regular Ternary Algebras

Utsanee Leerawat, Pradchaya Piajan

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.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|