The valuated ring of the arithmetical functions as a power series ring

Schwab, Emil Daniel, and Silberberg, Gheorghe. "The valuated ring of the arithmetical functions as a power series ring." Archivum Mathematicum 037.1 (2001): 77-80. <http://eudml.org/doc/248756>.

@article{Schwab2001,
abstract = {The paper examines the ring $A$ of arithmetical functions, identifying it to the domain of formal power series over $\{\bf C\}$ in a countable set of indeterminates. It is proven that $A$ is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that $A$ is a quasi-noetherian ring.},
author = {Schwab, Emil Daniel, Silberberg, Gheorghe},
journal = {Archivum Mathematicum},
keywords = {arithmetical function; valuated ring; formal power series; arithmetical function; valuated ring; ring of formal power series; complete ultrametric space; quasi-noetherian ring},
language = {eng},
number = {1},
pages = {77-80},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The valuated ring of the arithmetical functions as a power series ring},
url = {http://eudml.org/doc/248756},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Schwab, Emil Daniel
AU - Silberberg, Gheorghe
TI - The valuated ring of the arithmetical functions as a power series ring
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 1
SP - 77
EP - 80
AB - The paper examines the ring $A$ of arithmetical functions, identifying it to the domain of formal power series over ${\bf C}$ in a countable set of indeterminates. It is proven that $A$ is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that $A$ is a quasi-noetherian ring.
LA - eng
KW - arithmetical function; valuated ring; formal power series; arithmetical function; valuated ring; ring of formal power series; complete ultrametric space; quasi-noetherian ring
UR - http://eudml.org/doc/248756
ER -