The chain property for the associated primes of $\CA$-graded ideals

We investigate how the chain property for the associated primes of monomial degenerations of toric (or lattice) ideals can be generalized to arbitrary $\mathcal A$-graded monomial ideals. The generalization works in dimension $d=2$, but it fails for $d\geq 3$. Moreover, for a certain class of binomial ideals (including the $\mathcal A$-graded ones) we present an explicit cellular primary decomposition.

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Published 1 January 2000