The signature of a monomial ideal
The irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications beyond pure mathematics, such as biology. Given a monomial ideal $ I $ of a polynomial ring $ S = k[{\bf x}] $ over a field $ k $ and variables $ {\bf x} = \{x_1, \l...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-09-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241357?viewType=HTML |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850214971659517952 |
|---|---|
| author | Jovanny Ibarguen Daniel S. Moran Carlos E. Valencia Rafael H. Villarreal |
| author_facet | Jovanny Ibarguen Daniel S. Moran Carlos E. Valencia Rafael H. Villarreal |
| author_sort | Jovanny Ibarguen |
| collection | DOAJ |
| description | The irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications beyond pure mathematics, such as biology. Given a monomial ideal $ I $ of a polynomial ring $ S = k[{\bf x}] $ over a field $ k $ and variables $ {\bf x} = \{x_1, \ldots, x_n\} $, its incidence matrix, is the matrix whose rows are indexed by the variables $ {\bf x} $ and whose columns are indexed by its minimal generators. The main contribution of this paper is the introduction of a novel invariant of a monomial ideal $ I $, termed its signature, which could be thought of as a type of canonical form of its incidence matrix, and the proof that two monomial ideals with the same signature have essentially the same irreducible decomposition. |
| format | Article |
| id | doaj-art-0fca4fb5d360455380929acee24f42aa |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-0fca4fb5d360455380929acee24f42aa2025-08-20T02:08:44ZengAIMS PressAIMS Mathematics2473-69882024-09-01910279552797810.3934/math.20241357The signature of a monomial idealJovanny Ibarguen0Daniel S. Moran1Carlos E. Valencia2Rafael H. Villarreal3Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000, MéxicoDepartamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000, MéxicoDepartamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000, MéxicoDepartamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000, MéxicoThe irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications beyond pure mathematics, such as biology. Given a monomial ideal $ I $ of a polynomial ring $ S = k[{\bf x}] $ over a field $ k $ and variables $ {\bf x} = \{x_1, \ldots, x_n\} $, its incidence matrix, is the matrix whose rows are indexed by the variables $ {\bf x} $ and whose columns are indexed by its minimal generators. The main contribution of this paper is the introduction of a novel invariant of a monomial ideal $ I $, termed its signature, which could be thought of as a type of canonical form of its incidence matrix, and the proof that two monomial ideals with the same signature have essentially the same irreducible decomposition.https://www.aimspress.com/article/doi/10.3934/math.20241357?viewType=HTMLirreducible decompositionmonomial idealsignatureincidence matrixregular sequencesminimal free resolution |
| spellingShingle | Jovanny Ibarguen Daniel S. Moran Carlos E. Valencia Rafael H. Villarreal The signature of a monomial ideal AIMS Mathematics irreducible decomposition monomial ideal signature incidence matrix regular sequences minimal free resolution |
| title | The signature of a monomial ideal |
| title_full | The signature of a monomial ideal |
| title_fullStr | The signature of a monomial ideal |
| title_full_unstemmed | The signature of a monomial ideal |
| title_short | The signature of a monomial ideal |
| title_sort | signature of a monomial ideal |
| topic | irreducible decomposition monomial ideal signature incidence matrix regular sequences minimal free resolution |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241357?viewType=HTML |
| work_keys_str_mv | AT jovannyibarguen thesignatureofamonomialideal AT danielsmoran thesignatureofamonomialideal AT carlosevalencia thesignatureofamonomialideal AT rafaelhvillarreal thesignatureofamonomialideal AT jovannyibarguen signatureofamonomialideal AT danielsmoran signatureofamonomialideal AT carlosevalencia signatureofamonomialideal AT rafaelhvillarreal signatureofamonomialideal |