Antichains of Monomial Ideals are Finite

Details Antichains of Monomial Ideals are Finite Antichains of Monomial Ideals are Finite

1999-09-28

arxiv.org/abs/math/9909168v1

Mathematics

Commutative Algebra

8 pages

Scientific paper

The main result of this paper is that all antichains are finite in the poset
of monomial ideals in a polynomial ring, ordered by inclusion. We present
several corollaries of this result, both simpler proofs of results already in
the literature and new results. One natural generalization to more abstract
posets is shown to be false.

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