Constructions on P-Choice Algebras
I. Chajda and S. L. Wismath
P-compatibility is a structural property of identities introduced and studied by Plonka. Let P be a partition of the set of operation symbols of a fixed type t. An identitys sªt of a type t is called P-compatible if either s and t are the same variable, or s and t each start with operation symbols which belong to the same block (equivalence class) of the partition P. The concept of P-compatibility includes the two well-known special cases of normal identities and externally-compatible identities. Chajda’s characterization of the normalization of a variety by an algebraic construction called a choice algebra was generalized by Chajda, Denecke and Wismath to P-choice algebras, for any partition P. In this paper we consider algebraic constructions of homomorphic images, subalgebras and products on such P-choice algebras, and look at related class operators.