Finitely generated F-algebras with applications to Stein manifolds

E. R. Heal and Michael Windham

Vol. 51 (1974), No. 2, 459–465

DOI: 10.2140/pjm.1974.51.459

Abstract

Let A be a commutative n-generated F-algebra with identity, M_A the spectrum of A. Conditions are given which insure that M_A can be mapped homeomorphically into Cⁿ and that A is topologically isomorphic to the algebra of all holomorphic functions on a polynomially convex open subset of Cⁿ. A characterization is given of those Stein manifolds X for which p(X) is finitely generated.

Mathematical Subject Classification 2000

Primary: 32E25

Secondary: 32E10, 46J15

Milestones

Received: 15 February 1973

Published: 1 April 1974