Orderings of monomial ideals
Copyright policy )Orderings of monomial ideals
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute upper and lower bounds on the maximal order type.
40 pages
- University of Illinois at Urbana Champaign United States
- California State University, Dominguez Hills United States
- University of California, Berkeley United States
monomial ideals, polynomial ring, Hilbert-Samuel polynomials, Hilbert polynomials, 03E04; 06A07; 13D40, Mathematics - Logic, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 13D40, Polynomial rings and ideals; rings of integer-valued polynomials, Partial orders, general, reverse inclusion, Noetherian ordered set, 06A07, graded \(K\)-algebras, 03E04, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), invariants, Logic (math.LO), minimal order type, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
monomial ideals, polynomial ring, Hilbert-Samuel polynomials, Hilbert polynomials, 03E04; 06A07; 13D40, Mathematics - Logic, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 13D40, Polynomial rings and ideals; rings of integer-valued polynomials, Partial orders, general, reverse inclusion, Noetherian ordered set, 06A07, graded \(K\)-algebras, 03E04, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), invariants, Logic (math.LO), minimal order type, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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