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On Rings with a Certain Type of Factorization and Compact Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Pascual Cutillas Ripoll
Pascual Cutillas Ripoll*
Affiliation:
Dpto. de Matemáticas, Universidad de Salamanca, Spain
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Abstract

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Let be a compact Riemann surface, be the complement of a nonvoid finite subset of and A() be the ring of finite sums of meromorphic functions in with finite divisor. In this paper it is proved that every nonzero f ∈ A() can be decomposed as a product αβ, where α is either a unit or a product of powers of irreducible elements of A(), uniquely determined by f up to multiplication by units, and β is a product of functions of the type eφ – 1, with φ holomorphic and nonconstant in . Furthermore, a similar result is obtained for a certain class of subrings of A().

Keywords

30F1030D30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 1041 - 1052
Copyright
Copyright © Canadian Mathematical Society 1990

References

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