Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Border bases for lattice ideals   The main ingredient to construct an O-border basis of an ideal I $\subseteq$
K[x1,. .., xn] is the order ideal O, which is a basis of the K-vector space
K[x1,. .., xn]/I. In this paper we give a procedure to find all the possible
order ideals associated with a lattice ideal IM (where M is a lattice of Z n).
The construction can be applied to ideals of any dimension (not only
zero-dimensional) and shows that the possible order ideals are always in a
finite number. For lattice ideals of positive dimension we also show that,
although a border basis is infinite, it can be defined in finite terms.
Furthermore we give an example which proves that not all border bases of a
lattice ideal come from Gr\"obner bases. Finally, we give a complete and
explicit description of all the border bases for ideals IM in case M is a
2-dimensional lattice contained in Z 2 .

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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th