Finitely generated projective extensions of uniform algebras

Joan Manuel Verdera Melenchón

Vol. 100 (1982), No. 1, 203–215

DOI: 10.2140/pjm.1982.100.203

Abstract

Let A and B be uniform algebras and suppose that B is an extension of A, finitely generated and projective as an A-module. Let π denote the natural projection from the maximal ideal space of B onto the maximal ideal space of A. We show that K is a generalized peak interpolation set for B if and only if π(K) is a generalized peak interpolation set for A. Then we give a topological description of the maximals sets of antisymmetry of B in terms of those of A. Finally, we prove that if B is strongly separable over A, then the algebra of B-holomorphic functions is strongly separable over the algebra of A-holomorphic functions.

Mathematical Subject Classification 2000

Primary: 46J10

Secondary: 32E25

Milestones

Received: 1 October 1980

Revised: 4 March 1981

Published: 1 May 1982