The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
Snellman, Jan
Archivum Mathematicum, Tome 040 (2004), p. 161-179 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2004-01-01
Classification:  11A25,  13F25,  13J05 
@article{107898,
     author = {Jan Snellman},
     title = {The ring of arithmetical functions with unitary convolution: Divisorial and topological properties},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {161-179},
     zbl = {1122.11004},
     mrnumber = {2068688},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107898}
}

Snellman, Jan. The ring of arithmetical functions with unitary convolution: Divisorial and topological properties. Archivum Mathematicum, Tome 040 (2004) pp. 161-179. http://gdmltest.u-ga.fr/item/107898/

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