The join of varieties with associative-commutative intersection of bounded index.
In the present paper, by an algebra it is meant a linear algebra over a field of characteristic 0. The join of finitely-based varieties of algebras need not be finitely-based. The main result of the paper is the following theorem: Theorem 1. Let \(\mathcal A\) and \(\mathcal B\) be finitely-based varieties of algebras. Suppose that \(\mathcal A\cap\mathcal B\) is an associative commutative variety of algebras of index \(n\geq 3\). Then \(\mathcal A+\mathcal B\) is a finitely-based variety of algebras. -- Next, three open problems are proposed.
scientific article; zbMATH DE number 6485710