Geodesic
On Rings with a Certain Type of Factorization and Compact Riemann Surfaces
Canadian journal of mathematics, Tome 42 (1990) no. 6, pp. 1041-1052

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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().
DOI : 10.4153/CJM-1990-055-7
Mots-clés : 30F10, 30D30 
Ripoll, Pascual Cutillas. On Rings with a Certain Type of Factorization and Compact Riemann Surfaces. Canadian journal of mathematics, Tome 42 (1990) no. 6, pp. 1041-1052. doi: 10.4153/CJM-1990-055-7
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