Two semigroup rings associated to a finite set of germs of meromorphic functions

Abstract

We fix z 0 ∈ C and a field F with C ⊂ F ⊂ M z 0 := the field of germs of meromorphic functions at z 0 . We fix f 1 , . . . , f r ∈ M z 0 and we consider the F-algebrasWe present the general properties of the semigroup ringsand we tackle in detail the case in which F = M <1 is the field of meromorphic functions of order < 1 and f j 's are meromorphic functions over C of finite order with a finite number of zeros and poles. 2010 MSC: 30D30; 30D20; 16S36.