Geodesic
Arithmetic Funtions Over Rings with Zero Divisors
Bulletin of the Malaysian Mathematical Society, Tome 24 (2001) no. 1 
Pattira Ruangsinsap; Vichian Laohakosol; Pattanee Udomkavanich. Arithmetic Funtions Over Rings with
                        Zero Divisors. Bulletin of the Malaysian Mathematical Society, Tome 24 (2001) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2001_24_1_a8/
@article{BMMS_2001_24_1_a8,
     author = {Pattira Ruangsinsap and Vichian Laohakosol and Pattanee Udomkavanich},
     title = {Arithmetic {Funtions} {Over} {Rings} with
                        {Zero} {Divisors}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2001},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2001_24_1_a8/}
}
TY  - JOUR
AU  - Pattira Ruangsinsap
AU  - Vichian Laohakosol
AU  - Pattanee Udomkavanich
TI  - Arithmetic Funtions Over Rings with
                        Zero Divisors
JO  - Bulletin of the Malaysian Mathematical Society
PY  - 2001
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BMMS_2001_24_1_a8/
ID  - BMMS_2001_24_1_a8
ER  - 
%0 Journal Article
%A Pattira Ruangsinsap
%A Vichian Laohakosol
%A Pattanee Udomkavanich
%T Arithmetic Funtions Over Rings with
                        Zero Divisors
%J Bulletin of the Malaysian Mathematical Society
%D 2001
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/BMMS_2001_24_1_a8/
%F BMMS_2001_24_1_a8

Voir la notice de l'article provenant de la source BMMS

It is well known that the complex-valued arithmetic functions form a unique factorization domain under addition and convolution, and so do those functions with values in other suitable rings. Here we consider instead such functions with values in a unique factorization ring with zero divisors and prove that under certain yet similar conditions, they also form a unique factorization ring with zero divisors.