Antichains of monomial ideals are finite

Maclagan, Diane

doi:10.1090/S0002-9939-00-05816-0

Antichains of monomial ideals are finite
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by Diane Maclagan PDF

Proc. Amer. Math. Soc. 129 (2001), 1609-1615 Request permission

Abstract:

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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