Abstract
We characterize the finite distributive lattices on which there exists a unique compatible algebra with straightening laws.
Highlights
Let P be a finite partially ordered set and I( P) the distributive lattice of the poset ideals of P
In [3], it was shown that the toric ring K [O( P)] over a field K is an algebra with straightening laws (ASL in brief) on the distributive lattice I( P) over the field K
In [4], it was shown that the ring K [C( P)] associated with the chain polytope shares the same property
Summary
Let P be a finite partially ordered set (poset for short) and I( P) the distributive lattice of the poset ideals of P. Let K [Ω] ⊂ S be the toric ring generated over K by the set of monomials Ω = {ωα }α∈I( P) where ωα = wα t for all α ∈ I( P).
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