Coherence of some rings of functions

Abstract

To say that a commutative ring R with unit is coherent amounts to saying, in case R has no divisors of zero, that the intersection of two finitely generated ideals in R is finitely generated. We prove that the ring H∞ of bounded analytic functions in the unit disc is coherent, while the disc algebra A is not coherent. For any positive measure μ, L∞(μ) is coherent. © 1976.