Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4102
Title: Gröbner Bases for Submodules of $\mathbb Z^n$
Authors: Boffi, Giandomenico
Logar, Alessandro
Issue Date: 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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (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.
URI: http://hdl.handle.net/10077/4102
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.39 (2007)

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