Öz
Kaynakça
- S. S. Abhyankar, Local rings of high embedding dimension, Amer. J. Math., 89 (1967), 1073-1077.
- R. Apery, Sur les branches superlineaires des courbes algebriques, C. R. Acad. Sci. Paris, 222 (1946), 1198-2000.
- V. Barucci, D. E. Dobbs and M. Fontana, Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, Mem. Amer. Math. Soc., 125 (1997), 598 (78 pp).
- J. Bertin and P. Carbonne, Semi-groupes d'entiers et application aux branches, J. Algebra, 49(1) (1977), 81-95.
- V. Blanco and J. C. Rosales, The tree of irreducible numerical semigroup with fixed Frobenius number, Forum Math., 25(6) (2013), 1249-1261.
- W. C. Brown and J. Herzog, One dimensional local rings of maximal and almost maximal length, J. Algebra, 151 (1992), 332-347.
- J. Castellanos, A relation between the sequence of multiplicities and the semigroups of values of an algebroid curve, J. Pure Appl. Algebra, 43(2) (1986), 119-127.
- M. Delgado, P. A. Garcia-Sanchez and J. Morais, NumericalSgps, A package for numerical semigroups, Version 1.3.1 (2022), Refereed GAP package, \verb+ https://gap-packages.github.io/numericalsgps+.
- C. Delorme, Sous-monoides d'intersection complete de N, Ann. Scient. École Norm. Sup., (4)9 (1976), 145-154.
- The GAP group, GAP-Groups, Algorithms, and Programming, Version 4.12.2, 2022, \verb+https://www.gap-system.org+.
- E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc., 25 (1970), 748-751.
- M. A. Moreno-Frias and J. C. Rosales, Ratio-covariety of numerical semigroups, Axioms, 13(3) (2024), 193 (13 pp).
- J. C. Rosales, Principal ideals of numerical semigroups, Bull. Belg. Math. Soc., 10 (2003), 329-343.
- J. C. Rosales and M. B. Branco, Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups, J. Pure Appl. Algebra, 171 (2002), 303-314.
- J. C. Rosales and M. B. Branco, Irreducible numerical semigroups, Pacific J. Math., 209 (2003), 131-143.
- J. C. Rosales and P. A. Garcia-Sanchez, Numerical Semigroups, Developments in Mathematics, Vol. 20, Springer, New York, 2009.
- J. C. Rosales, P. A. Garcia-Sanchez, J. I. Garcia-Garcia and M. B. Branco, Numerical semigroups with maximal embedding dimension, Int. J. Commut. Rings, 2 (2003), 47-53.
- J. D. Sally, Cohen-Macaulay local rings of maximal embedding dimension, J. Algebra, 56 (1979), 168-183.
- K. Watanabe, Some examples of one dimensional Gorenstein domains, Nagoya Math. J., 49 (1973), 101-109.
The ratio-covariety of numerical semigroups having maximal embedding dimension with fixed multiplicity and Frobenius number
Öz
In this paper we will show that
MED$(F,m)=\{S\mid S \mbox{ is a numerical semigroup with maximal embedding dimension, Frobenius number} ~F~ \mbox{and multiplicity}~ m\}$ is a ratio-covariety. As a consequence, we present two algorithms: one that computes MED$(F,m)$ and another one that calculates the elements of MED$(F,m)$ with a given genus.
If $X\subseteq S\backslash (\langle m \rangle \cup \{F+1,\rightarrow\})$ for some $S\in $ MED$(F,m)$, then there exists the smallest element of MED$(F,m)$ containing $X$. This element will be denoted by MED$(F,m)[X]$ and we will say that $X$ one of its MED$(F,m)$-system of generators. We will prove that every element $S$ of MED$(F,m)$ has a unique minimal MED$(F,m)$-system of generators and it will be denoted by MED$(F,m)$msg$(S).$ The cardinality of MED$(F,m)$msg$(S)$, will be called MED$(F,m)$-rank of $S.$ We will also see in this work, how all the elements of MED$(F,m)$ with a fixed MED$(F,m)$-rank are.
Anahtar Kelimeler
Numerical semigroup ratio-covariety Frobenius number genus multiplicity algorithm
Kaynakça
- S. S. Abhyankar, Local rings of high embedding dimension, Amer. J. Math., 89 (1967), 1073-1077.
- R. Apery, Sur les branches superlineaires des courbes algebriques, C. R. Acad. Sci. Paris, 222 (1946), 1198-2000.
- V. Barucci, D. E. Dobbs and M. Fontana, Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, Mem. Amer. Math. Soc., 125 (1997), 598 (78 pp).
- J. Bertin and P. Carbonne, Semi-groupes d'entiers et application aux branches, J. Algebra, 49(1) (1977), 81-95.
- V. Blanco and J. C. Rosales, The tree of irreducible numerical semigroup with fixed Frobenius number, Forum Math., 25(6) (2013), 1249-1261.
- W. C. Brown and J. Herzog, One dimensional local rings of maximal and almost maximal length, J. Algebra, 151 (1992), 332-347.
- J. Castellanos, A relation between the sequence of multiplicities and the semigroups of values of an algebroid curve, J. Pure Appl. Algebra, 43(2) (1986), 119-127.
- M. Delgado, P. A. Garcia-Sanchez and J. Morais, NumericalSgps, A package for numerical semigroups, Version 1.3.1 (2022), Refereed GAP package, \verb+ https://gap-packages.github.io/numericalsgps+.
- C. Delorme, Sous-monoides d'intersection complete de N, Ann. Scient. École Norm. Sup., (4)9 (1976), 145-154.
- The GAP group, GAP-Groups, Algorithms, and Programming, Version 4.12.2, 2022, \verb+https://www.gap-system.org+.
- E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc., 25 (1970), 748-751.
- M. A. Moreno-Frias and J. C. Rosales, Ratio-covariety of numerical semigroups, Axioms, 13(3) (2024), 193 (13 pp).
- J. C. Rosales, Principal ideals of numerical semigroups, Bull. Belg. Math. Soc., 10 (2003), 329-343.
- J. C. Rosales and M. B. Branco, Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups, J. Pure Appl. Algebra, 171 (2002), 303-314.
- J. C. Rosales and M. B. Branco, Irreducible numerical semigroups, Pacific J. Math., 209 (2003), 131-143.
- J. C. Rosales and P. A. Garcia-Sanchez, Numerical Semigroups, Developments in Mathematics, Vol. 20, Springer, New York, 2009.
- J. C. Rosales, P. A. Garcia-Sanchez, J. I. Garcia-Garcia and M. B. Branco, Numerical semigroups with maximal embedding dimension, Int. J. Commut. Rings, 2 (2003), 47-53.
- J. D. Sally, Cohen-Macaulay local rings of maximal embedding dimension, J. Algebra, 56 (1979), 168-183.
- K. Watanabe, Some examples of one dimensional Gorenstein domains, Nagoya Math. J., 49 (1973), 101-109.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 30 Ekim 2024 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 14 Ocak 2024 |
| Kabul Tarihi | 18 Eylül 2024 |
| Yayımlandığı Sayı | Yıl 2025 Early Access |