Narrow Results

P-Compatibility is a hereditary property of identities which generalizes the properties of normality and externality of identities. Chajda characterized the normalization of a variety by an algebraic construction called a choice algebra. In this paper, we generalize this characterization to the least P-compatible variety P(V) determined by a variety V for any partition P using P-choice algebras. We also study the clone of (strongly) P-compatible n-ary terms of a variety V, and relate identities of this clone to (strongly) P-compatible hyperidentities of the variety V.

A functional Menger ∩-algebra is a set of n-place functions containing n projections and closed under the so-called Menger's composition of n-place functions and the set-theoretic intersection of functions. We give the abstract characterization for these subsets of functional Menger ∩-algebras which contain functions with fixed points.