Geodesic
The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
Archivum mathematicum, Tome 40 (2004) no. 2, pp. 161-179.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study $(\mathcal {A},+,\oplus )$, the ring of arithmetical functions with unitary convolution, giving an isomorphism between $(\mathcal {A},+,\oplus )$ and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] between the ring $(\mathcal {A},+,\cdot )$ of arithmetical functions with Dirichlet convolution and the power series ring $ [\![x_1,x_2,x_3,\dots ]\!]$ on countably many variables. We topologize it with respect to a natural norm, and show that all ideals are quasi-finite. Some elementary results on factorization into atoms are obtained. We prove the existence of an abundance of non-associate regular non-units.
Classification : 11A25, 13F25, 13J05
Keywords: unitary convolution; Schauder Basis; factorization into atoms; zero divisors 
@article{ARM_2004__40_2_a3,
     author = {Snellman, Jan},
     title = {The ring of arithmetical functions with unitary convolution: {Divisorial} and topological properties},
     journal = {Archivum mathematicum},
     pages = {161--179},
     publisher = {mathdoc},
     volume = {40},
     number = {2},
     year = {2004},
     mrnumber = {2068688},
     zbl = {1122.11004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2004__40_2_a3/}
}
TY  - JOUR
AU  - Snellman, Jan
TI  - The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
JO  - Archivum mathematicum
PY  - 2004
SP  - 161
EP  - 179
VL  - 40
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_2004__40_2_a3/
LA  - en
ID  - ARM_2004__40_2_a3
ER  - 
%0 Journal Article
%A Snellman, Jan
%T The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
%J Archivum mathematicum
%D 2004
%P 161-179
%V 40
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_2004__40_2_a3/
%G en
%F ARM_2004__40_2_a3
Snellman, Jan. The ring of arithmetical functions with unitary convolution: Divisorial and topological properties. Archivum mathematicum, Tome 40 (2004) no. 2, pp. 161-179. http://geodesic.mathdoc.fr/item/ARM_2004__40_2_a3/