On rings with a certain type of factorization and compact Riemann surfaces
- 1 Dpto. de Matemáticas, Universidad de Salamanca, Spain
ISSN: 0008-414X, 1496-4279
Año de publicación: 1990
Volumen: 42
Número: 6
Páginas: 1041-1052
Tipo: Artículo
Otras publicaciones en: Canadian Journal of Mathematics
Resumen
Let V be a compact Riemann surface, V' be the complement of a nonvoid finite subset of V and A(V') be the ring of finite sums of meromorphic functions in V' with finite divisor. In this paper it is proved that every nonzero f element-of A(V') can be decomposed as a product alpha-beta, where-alpha is either a unit or a product of powers of irreducible elements of A(V'), uniquely determined by f up to multiplication by units, and beta is a product of functions of the type e-phi - 1, with phi-holomorphic and nonconstant in V'. Furthermore, a similar result is obtained for a certain class of subrings of A(V').
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