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Gröbner Bases for Submodules of $\mathbb Z^n$
Boffi, Giandomenico
Logar, Alessandro
2007
Abstract
We define Gröbner bases for submodules of $\mathbb Z^n$ and
characterize minimal and reduced bases combinatorially in terms
of minimal elements of suitable partially ordered subsets of $\mathbb Z^n$.
Then we show that Gröbner bases for saturated pure binomial
ideals of K[x_1, . . . , x_n], char (K) ≠ 2, can be immediately derived
from Gröbner bases for appropriate corresponding submodules
of $\mathbb Z^n$. This suggests the possibility of calculating the Gröbner
bases of the ideals without using the Buchberger algorithm.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Publisher
EUT Edizioni Università di Trieste
Source
Giandomenico Boffi, Alessandro Logar, "Gröbner Bases for Submodules of $\mathbb Z^n$", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 39 (2007), pp. 43-62.
Languages
en
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