Primitive varieties of algebras
Let \(\Omega \) be a set of finitary functional symbols and \(f,g \in \Omega \). Then \(f(x_1,\ldots ,x_n)=g(x_1,\ldots ,x_m)\) is called a primitive identity. A set \(\Sigma \) of primitive identities is closed if \(\Sigma \models \Sigma '\) implies \(\Sigma ' \subseteq \Sigma \). A variety \(V\) is primitive if it is defined by a set of primitive identities. The main results are descriptions of closed sets of primitive identities and of free objects of primitive varieties.
scientific article; zbMATH DE number 1407074