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Primary Decomposition of Lattice Basis Ideals

✍ Scribed by Serkan Hoşten; Jay Shapiro

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
281 KB
Volume
29
Category
Article
ISSN
0747-7171

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✦ Synopsis

We study the primary decomposition of lattice basis ideals. These ideals are binomial ideals with generators given by the elements of a basis of a saturated integer lattice. We show that the minimal primes of such an ideal are completely determined by the sign pattern of the basis elements, while the embedded primes are not. As a special case we examine the ideal generated by the 2 × 2 adjacent minors of a generic m × n matrix. In particular, we determine all minimal primes in the 3 × n case. We also present faster ways of computing a generating set for the associated toric ideal from a lattice basis ideal.

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