Coherence of some rings of functions |
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Authors: | WS McVoy LA Rubel |
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Institution: | University of Illinois, Urbana-Champaign, Illinois 61801 USA |
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Abstract: | To say that a commutative ring with unit is coherent amounts to saying, in case has no divisors of zero, that the intersection of two finitely generated ideals in 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. |
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