Geodesic
Truncations of the ring of number-theoretic functions
Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 17-27.

Voir la notice de l'article provenant de la source International Press of Boston

We study the ring $\Gamma$ of all functions ${\mathbb{N}}^+ \to K$, endowed with the usual convolution product. $\Gamma$, which we call the ring of number-theoretic functions, is an inverse limit of the “truncations” \[ \Gamma_n = \{ f \in \Gamma \mid \forall m > n: \, f(m)=0 \}. \] Each $\Gamma_n$ is a zero-dimensional, finitely generated $K$-algebra, which may be expressed as the quotient of a finitely generated polynomial ring with a stable (after reversing the order of the variables) monomial ideal. Using the description of the free minimal resolution of stable ideals given by Eliahou-Kervaire, and some additional arguments by Aramova-Herzog and Peeva, we give the Poincaré-Betti series for $\Gamma_n$.
DOI : 10.4310/HHA.2000.v2.n1.a2
Classification : 13Dxx
Keywords: ring of number theoretic functions, Poincaré-Betti series, stable monomial ideals 
@article{HHA_2000_2_1_a2,
     author = {Jan Snellman},
     title = {Truncations of the ring of number-theoretic functions},
     journal = {Homology, homotopy, and applications},
     pages = {17--27},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2000},
     doi = {10.4310/HHA.2000.v2.n1.a2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a2/}
}
TY  - JOUR
AU  - Jan Snellman
TI  - Truncations of the ring of number-theoretic functions
JO  - Homology, homotopy, and applications
PY  - 2000
SP  - 17
EP  - 27
VL  - 2
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a2/
DO  - 10.4310/HHA.2000.v2.n1.a2
LA  - en
ID  - HHA_2000_2_1_a2
ER  - 
%0 Journal Article
%A Jan Snellman
%T Truncations of the ring of number-theoretic functions
%J Homology, homotopy, and applications
%D 2000
%P 17-27
%V 2
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a2/
%R 10.4310/HHA.2000.v2.n1.a2
%G en
%F HHA_2000_2_1_a2
Jan Snellman. Truncations of the ring of number-theoretic functions. Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 17-27. doi : 10.4310/HHA.2000.v2.n1.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a2/

Cité par Sources :