On \(n\)-clone extensions of algebras
An identity \(\varphi \approx \psi \) is clone compatible if either \(\varphi \) and \(\psi \) are the same variable or the sets of fundamental operations in \(\varphi \) and \(\psi \) are nonempty and identical. The author constructs an \(n\)-clone extension of a given algebra and for a variety \(V\) he denotes by \(V^c\) the variety defined by all clone compatible identities from Id\((V)\) and by \(V^{c,n}\) the \(n\)-clone extension of \(V\). The paper contains representations of algebras from \(V^c\) and \(V^{c,n}\) under certain assumptions. The results are applied to several important varieties including the variety of distributive lattices and the variety of Boolean algebras.
scientific article; zbMATH DE number 1407100