| Title:
|
The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated (English) |
| Author:
|
Moreno-Frías, Maria Angeles |
| Author:
|
Rosales, José Carlos |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
439-454 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Delta $ be a numerical semigroup. In this work we show that $\mathcal {J}(\Delta ) =\{I\cup \nobreak \{0\}\colon I \mbox { is an ideal of } \Delta \}$ is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set $\mathcal {J}_a(\Delta )=\{S\in \mathcal {J}(\Delta )\colon \max (\Delta \backslash S)=a\}$ for a given $a\in \Delta .$ As a consequence, we obtain another algorithm that computes all the elements of $\mathcal {J}(\Delta )$ with a fixed genus. (English) |
| Keyword:
|
numerical semigroup |
| Keyword:
|
ideal |
| Keyword:
|
Frobenius restricted variety |
| Keyword:
|
embedding dimension |
| Keyword:
|
Frobenius number |
| Keyword:
|
restricted Frobenius number |
| Keyword:
|
genus |
| Keyword:
|
multiplicity |
| Keyword:
|
Arf numerical semigroup |
| Keyword:
|
saturated semigroup |
| MSC:
|
11Y16 |
| MSC:
|
20M14 |
| DOI:
|
10.21136/MB.2023.0038-23 |
| . |
| Date available:
|
2024-09-11T13:50:14Z |
| Last updated:
|
2024-09-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152544 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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