# The ring of arithmetical functions with unitary convolution: Divisorial and topological properties

Archivum Mathematicum (2004)

- Volume: 040, Issue: 2, page 161-179
- ISSN: 0044-8753

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topSnellman, Jan. "The ring of arithmetical functions with unitary convolution: Divisorial and topological properties." Archivum Mathematicum 040.2 (2004): 161-179. <http://eudml.org/doc/249297>.

@article{Snellman2004,

abstract = {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.},

author = {Snellman, Jan},

journal = {Archivum Mathematicum},

keywords = {unitary convolution; Schauder Basis; factorization into atoms; zero divisors; Schauder basis; factorization into atoms; zero divisors},

language = {eng},

number = {2},

pages = {161-179},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {The ring of arithmetical functions with unitary convolution: Divisorial and topological properties},

url = {http://eudml.org/doc/249297},

volume = {040},

year = {2004},

}

TY - JOUR

AU - Snellman, Jan

TI - The ring of arithmetical functions with unitary convolution: Divisorial and topological properties

JO - Archivum Mathematicum

PY - 2004

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 040

IS - 2

SP - 161

EP - 179

AB - 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.

LA - eng

KW - unitary convolution; Schauder Basis; factorization into atoms; zero divisors; Schauder basis; factorization into atoms; zero divisors

UR - http://eudml.org/doc/249297

ER -

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