n-Algebraic Complete Algebras, Pseudodirect Products, and the Algebraic Closure Operator on Subsets of Universal Algebras

Abstract

We introduce the notions of n-algebraic complete algebras and n-algebraic completeness, which makes it possible to find algebraic closures of subsets of universal algebras. We clarify how the n-algebraic completeness of an algebra is connected with the pseudodirect product of algebras.