Abstract
Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.
Highlights
In 1946, Menger, K. [1] studied the algebraic properties of the composition of multiplace functions
We first introduce the notion of ternary Menger algebras of rank n which can be regarded as a canonical generalization of arbitrary ternary semigroups in a different sense from n-ary semigroups
We introduce some special elements on a ternary Menger algebra, and show the relationship between a diagonal ternary semigroup and a ternary Menger algebra of rank n
Summary
In 1946, Menger, K. [1] studied the algebraic properties of the composition of multiplace functions. The property of the composition, which is called superassociative law, was studied in both primary and advanced ways By using this idea, the concept of Menger algebras of rank n, for all natural numbers n (sometimes, it is called superassociative algebras) was presented. S. who studied the so-called principal v-congruences on Menger algebras of rank n, which are the generalizations of the principal right and left congruences on arbitrary semigroups (see [3]). M. [8] studied the problem of characterizing inner translations on semigroups Based on these knowledge, Kumduang, T. and Leeratanavalee, S. introduced the notion of the left translations for Menger algebras of rank n and studied some of its algebraic properties. We first introduce the notion of ternary Menger algebras of rank n which can be regarded as a canonical generalization of arbitrary ternary semigroups in a different sense from n-ary semigroups.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
