On rings with a certain type of factorization and compact Riemann surfaces

  1. Pascual Cutillas Ripoll 1
  1. 1 Dpto. de Matemáticas, Universidad de Salamanca, Spain
Aldizkaria:
Canadian Journal of Mathematics

ISSN: 0008-414X,  1496-4279

Argitalpen urtea: 1990

Alea: 42

Zenbakia: 6

Orrialdeak: 1041-1052

Mota: Artikulua

DOI: 10.4153/CJM-1990-055-7 GOOGLE SCHOLAR lock_openSarbide irekia editor

Beste argitalpen batzuk: Canadian Journal of Mathematics

Laburpena

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').

Erreferentzia bibliografikoak

  • Kra, Automorphic functions and kleinian groups
  • Cutillas Ripoll, (1986), On the isomorphisms between certain function fields over compact Riemann surfaces,, 275, pp. 81
  • 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