Distributed families of varieties of algebras (Q1087573)

Let \(\{V_ p\}_{p\in P}\) be a family of varieties of algebras, where \(V_ p\) contains algebras of type \(\tau_ p\). In this paper each \(V_ p\) is replaced by a variety \(K_ p\) of type \(\tau\), where \(\tau\) is a common extension of the \(\tau_ p\) and each algebra in \(K_ p\) is obtained by adjoining a constant to an algebra in \(V_ p\). It is shown that under certain conditions on the family \(\{K_ p\}_{p\in P}\) its join consists of algebras which are subdirect products of algebras from \(\cup K_ p\) and from one other variety. An equational basis of this join is also constructed.