Monomial ideals with large projective dimension
| Autor: | Guillermo Alesandroni |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Monomial
Algebra and Number Theory Degree (graph theory) Mathematics::Commutative Algebra Betti number Polynomial ring 010102 general mathematics Dimension (graph theory) Field (mathematics) Characterization (mathematics) Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences Combinatorics 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics |
| Popis: | Let S be a polynomial ring in n variables, over an arbitrary field. Let M be the family of all monomial ideals in S. Using combinatorial methods, we give an explicit characterization of all M ∈ M , such that pd ( S / M ) = n . In addition, we give the total, graded, and multigraded Betti numbers of S / M in homological degree n, for all M ∈ M . Finally, we show that for each M ∈ M , with pd ( S / M ) = n , the sum of the total Betti numbers of S / M is at least 2 n . |
| Databáze: | OpenAIRE |
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