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| Paper IPM / M / 15375 |
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| Abstract: | |
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For two given finite lattices L and M, we introduce the ideal of lattice homomorphism
J(L, M), whose minimal monomial generators correspond to lattice
homomorphisms Ï : L â M. We show that L is a distributive lattice if and only
if the equidimensinal part of J(L, M) is the same as the equidimensional part of
the ideal of poset homomorphisms I(L, M). Next, we study the minimal primary
decomposition of J(L, M) when L is a distributive lattice and M = [2]. We present
some methods to check if a monomial prime ideal belongs to ass(J(L, [2])), and we
give an upper bound in terms of combinatorial properties of L for the height of
the minimal primes. We also show that if each minimal prime ideal of J(L, [2])
has height at most three, then L is a planar lattice and width(L) 6 2. Finally, we
compute the minimal primary decomposition when L = [m] Ã [n] and M = [2].
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