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The Riemann surface of a ring

Published online by Cambridge University Press:  09 April 2009

M. G. Stanley
M. G. Stanley
Affiliation:
Case Western Reserve UniversityCleveland, Ohio
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The contravariant functor F from the category of Riemann surfaces and analytic mappings to the category of complex algebras and homomorphisms which takes each surface Ω to the algebra of analytic functions on Ω does not have an adjoint on the right; but it nearly does. To each algebra A there is associated a surface Σ1 (A) and a homomorphism A from A into FΣ1 (A), indeed onto an algebra of functions not all of which are constant on any component of Σ1 (A), such that every such non-trivial representation A A → F(Ω) is induced by a unique analytic mapping Ω → Σ1(A)

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 251 - 256
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Isbell, J., ‘Structure of categories’, Bull. Amer. Math. Soc. 72, (1966), 619–655.Google Scholar
[2]Lambek, J., Completions of Categories ( Springer Lecture Notes 24, Berlin, 1966).CrossRefGoogle Scholar
[3]Richards, I., ‘A criterion for rings of analytic functions’, Trans. Amer. Math. Soc. 128, (1967), 523–530.Google Scholar