Mathematical Research Letters
Volume 7 (2000)
The chain property for the associated primes of $\CA$-graded ideals
Pages: 565 – 575
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.