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Two semigroup rings associated to a finite set of meromorphic functions

In: Mathematica Slovaca, vol. 70, no. 5
Mircea Cimpoeaş
Detaily:
Rok, strany: 2020, 1249 - 1257
Kľúčové slová:
meromorphic functions, entire functions, semigroup rings
O článku:
We fix $z0\in\mathbb C$ and a field $\mathbb F$ with $\mathbb C\subset \mathbb F \subset \mathcal Mz0:=$ the field of germs of meromorphic functions at $z0$. We fix $f1,…,fr\in \mathcal Mz0$ and we consider the $\mathbb F$-algebras $S:=\mathbb F[f1,…,fr]$ and $\overline S:=\mathbb F[f1\pm 1,…,fr\pm 1]$. We present the general properties of the semigroup rings

$$ Shol:=\mathbb F[f\mathbf a:=f1a1… frar: (a1,…,ar)\in\mathbb Nr andf\mathbf ais holomorphic atz0], $$

$$ \overline Shol:=\mathbb F[f\mathbf a:=f1a1… frar: (a1,…,ar)\in\mathbb Zr andf\mathbf ais holomorphic atz0], $$

and we tackle in detail the case $\mathbb F=\mathcal M<1$, the field of meromorphic functions of order $<1$, and $fj$'s are meromorphic functions over $\mathbb C$ of finite order with a finite number of zeros and poles.
Ako citovať:
ISO 690:
Cimpoeaş, M. 2020. Two semigroup rings associated to a finite set of meromorphic functions. In Mathematica Slovaca, vol. 70, no.5, pp. 1249-1257. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0428

APA:
Cimpoeaş, M. (2020). Two semigroup rings associated to a finite set of meromorphic functions. Mathematica Slovaca, 70(5), 1249-1257. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0428
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 27. 9. 2020