The Menger algebra of terms induced by order-decreasing transformations
Khwancheewa Wattanatripop, Thawhat Changphas · Communications in Algebra · 2021
Let τn be a type of algebras with the n-ary operation symbols, for a fixed integer n≥1. In this article, we introduce terms of type τn called order-decreasing full terms. We prove that the set of all order-decreasing full terms of type τn is closed under the superposition operation; and hence it forms an algebra denoted by MAODn(τn). Moreover, we prove that MAODn(τn) is a Menger algebra of rank n. Finally, we introduce and study order-decreasing full hypersubstitutions and the related order-decreasing full closed identities and order-decreasing full closed varieties.