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
Datum der Publikation: 1990
Ausgabe: 42
Nummer: 6
Seiten: 1041-1052
Art: Artikel
Andere Publikationen in: Canadian Journal of Mathematics
Zusammenfassung
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').
Bibliographische Referenzen
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- Bourbaki, (1965), Commutative algebra
- Cutillas Ripoll, (1984), Construction of certain function fields associated with a compact Riemann surface, 106, pp. 1423
- Dubrovin, (1981), Theta functions and nonlinear equations, 36, pp. 11
- Farkas, Riemann Surfaces