On generalizations of C*-embedding for wallman rings

Abstract

Biles (1970) has called a subring A of the ring C(X), of all real valued continuous functions on a topological space X, a Wallman ring on X whenever Z(A), the zero sets of functions belonging to A, forms a normal base on A'in the sense of Frink (1964). Previously, we have related algebraic properties of a Wallman ring A to topological properties of the Wallman compactification w(Z(A)) of X determined by the normal base Z{A). Here we introduce two different generalizations of the concept of "a C*-embedded subset" and study relationships between these and topological (respectively, algebraic) properties of w(Z(A)) (respectively, A).