We define Gr ̈bner bases for submodules of Zn and o characterize minimal and reduced bases combinatorially in terms of minimal elements of suitable partially ordered subsets of Zn . Then we show that Gr ̈bner bases for saturated pure binomial o ideals of K[x1 , . . . , xn ], char (K) = 2, can be immediately de- rived from Gr ̈bner bases for appropriate corresponding submod- o ules of Zn . This suggests the possibility of calculating the Gr ̈bner o bases of the ideals without using the Buchberger algorithm
Groebner bases for submodules of Z^n / G., Boffi; Logar, Alessandro. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - STAMPA. - XXXIV:(2007), pp. 43-62.
Groebner bases for submodules of Z^n
LOGAR, ALESSANDRO
2007-01-01
Abstract
We define Gr ̈bner bases for submodules of Zn and o characterize minimal and reduced bases combinatorially in terms of minimal elements of suitable partially ordered subsets of Zn . Then we show that Gr ̈bner bases for saturated pure binomial o ideals of K[x1 , . . . , xn ], char (K) = 2, can be immediately de- rived from Gr ̈bner bases for appropriate corresponding submod- o ules of Zn . This suggests the possibility of calculating the Gr ̈bner o bases of the ideals without using the Buchberger algorithmPubblicazioni consigliate
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