Clone networks, clone extensions and biregularizations of varieties of algebras (Q2762293)

Let \(V\) be a variety of algebras of type \(\tau\), where \(0\notin \tau\neq\emptyset\). An identity \(\phi\approx\psi\) is said to be clone-compatible if \(\phi\) and \(\psi\) are the same variable, or if the same (non-empty) set of fundamental operations occurs on both sides. The set of clone compatible identities of \(V\) is not necessarily an equational theory, but we can consider the variety \(V^c\) which it defines. This paper introduces a construction, called a clone network (unfortunately, rather too technical to give here), which enables one to describe the members of \(V^c\) in terms of those of \(V\).