Besides a self-contained introduction into well quasi-orders and better quasi-orders, the focus is on how these concepts lead in a neat and quick way to some well-known facts regarding monomials and monomial ideals of a polynomial ring over a field. Not uninteresting connections emerge, such as a direct path to Dickson’s lemma for monomial ideals from Higman’s theorem for monoids of terms in the vein of Hilbert’s basis theorem in iterative form.
Well quasi-orders, better quasi-orders, and monomial ideals
Buriola, Gabriele
;Schuster, Peter
2025-01-01
Abstract
Besides a self-contained introduction into well quasi-orders and better quasi-orders, the focus is on how these concepts lead in a neat and quick way to some well-known facts regarding monomials and monomial ideals of a polynomial ring over a field. Not uninteresting connections emerge, such as a direct path to Dickson’s lemma for monomial ideals from Higman’s theorem for monoids of terms in the vein of Hilbert’s basis theorem in iterative form.
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