Abstract
In this paper, some special varieties which generalize Jónsson–Tarski algebras are considered. We prove that every nontrivial algebra from such a variety is term infinite and contains infinitely many distinct proper diagonal term operations of every arity.
Highlights
On algebras (A; ·, ∗) of type (2, 1, 1) with |A| ≥ 2
Note that Cantor identities have been considered in connection with the investigation of algebras with bases of different cardinalities
If A is a nontrivial algebra from A1,n, the algebra II (A) is term infinite
Summary
Note that Cantor identities have been considered in connection with the investigation of algebras with bases of different cardinalities. Stronger result: the number of distinct essentially n-ary term operations of these algebras is infinite for every n. In this connection, for every positive integer n, we consider the variety A1,n of algebras Fn, g) is a nontrivial algebra from the variety A1,n, there exist infinitely many distinct proper k-ary diagonal term operations in Pk(A) for all k > 1. It follows immediately that every nontrivial algebra A from A1,n is term infinite. Dudek [2] (P 1083 of New Scottish Book), we conjecture the following: Problem 1.4. If A is a nontrivial algebra from the variety Am,n, where m < n, the algebra II(A) is term infinite
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