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Licensed Unlicensed Requires Authentication Published by De Gruyter September 27, 2020

Two semigroup rings associated to a finite set of meromorphic functions

  • Mircea Cimpoeaş EMAIL logo
From the journal Mathematica Slovaca

Abstract

We fix z0 ∈ ℂ and a field 𝔽 with ℂ ⊂ 𝔽 ⊂ 𝓜z0 := the field of germs of meromorphic functions at z0. We fix f1, …, fr ∈ 𝓜z0 and we consider the 𝔽-algebras S := 𝔽[f1, …, fr] and S¯:=F[f1±1,,fr±1]. We present the general properties of the semigroup rings

Shol:=F[fa:=f1a1frar:(a1,,ar)Nr and fa is holomorphic at z0],S¯hol:=F[fa:=f1a1frar:(a1,,ar)Zr and fa is holomorphic at z0],

and we tackle in detail the case 𝔽 = 𝓜<1, the field of meromorphic functions of order < 1, and fj’s are meromorphic functions over ℂ of finite order with a finite number of zeros and poles.

  1. (Communicated by Stanisława Kanas)

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Received: 2019-10-29
Accepted: 2020-01-22
Published Online: 2020-09-27
Published in Print: 2020-10-27

© 2020 Mathematical Institute Slovak Academy of Sciences

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