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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. |
Type: | Article | 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) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| BoffiLogarRendMat39.pdf | 192 kB | Adobe PDF |  View/Open |
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