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STAR OPERATIONS ON KUNZ DOMAINS

Yıl 2019, , 171 - 185, 08.01.2019
https://doi.org/10.24330/ieja.504142

Öz

We study star operations on Kunz domains, a class of analyti-
cally irreducible, residually rational domains associated to pseudo-symmetric
numerical semigroups, and we use them to refute a conjecture of Houston, Mi-
mouni and Park. We also nd an estimate for the number of star operations
in a particular case, and a precise counting in a sub-case.

Kaynakça

  • 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(598) (1997), x+78 pp.
  • H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
  • E. G. Houston, A. Mimouni and M. H. Park, Integral domains which admit at most two star operations, Comm. Algebra, 39(5) (2011), 1907-1921.
  • E. G. Houston, A. Mimouni and M. H. Park, Noetherian domains which admit only nitely many star operations, J. Algebra, 366 (2012), 78-93.
  • E. G. Houston, A. Mimouni and M. H. Park, Integrally closed domains with only nitely many star operations, Comm. Algebra, 42(12) (2014), 5264-5286.
  • E. Houston, A. Mimouni and M. H. Park, Star operations on overrings of Noetherian domains, J. Pure Appl. Algebra, 220(2) (2016), 810-821.
  • E. Houston, A. Mimouni and M. H. Park, Star operations on overrings of Prufer domains, Comm. Algebra, 45(8) (2017), 3297-3309.
  • E. G. Houston and M. H. Park, A characterization of local Noetherian domains which admit only nitely many star operations: The in nite residue eld case, J. Algebra, 407 (2014), 105-134.
  • J. Jager, Langenberechnung und kanonische Ideale in eindimensionalen Ringen, Arch. Math. (Basel), 29(5) (1977), 504-512.
  • E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc., 25 (1970), 748-751.
  • E. Kunz, Beispiel: Die kanonische Idealklasse eines eindimensionalen Cohen- Macaulay-Rings, 103, Lecture Notes in Math., Vol. 238, Springer, Berlin, (1971), 17-24.
  • T. Matsuoka, On the degree of singularity of one-dimensional analytically irreducible Noetherian local rings, J. Math. Kyoto Univ., 11 (1971), 485-494.
  • J. C. Rosales and P. A. Garca-Sanchez, Numerical Semigroups, Developments in Mathematics, 20, Springer, New York, 2009.
  • D. Spirito, Star operations on numerical semigroups, Comm. Algebra, 43(7) (2015), 2943-2963.
  • B. White, Star Operations and Numerical Semigroup Rings, Ph.D. thesis, The University of New Mexico, 2014.
Yıl 2019, , 171 - 185, 08.01.2019
https://doi.org/10.24330/ieja.504142

Öz

Kaynakça

  • 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(598) (1997), x+78 pp.
  • H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
  • E. G. Houston, A. Mimouni and M. H. Park, Integral domains which admit at most two star operations, Comm. Algebra, 39(5) (2011), 1907-1921.
  • E. G. Houston, A. Mimouni and M. H. Park, Noetherian domains which admit only nitely many star operations, J. Algebra, 366 (2012), 78-93.
  • E. G. Houston, A. Mimouni and M. H. Park, Integrally closed domains with only nitely many star operations, Comm. Algebra, 42(12) (2014), 5264-5286.
  • E. Houston, A. Mimouni and M. H. Park, Star operations on overrings of Noetherian domains, J. Pure Appl. Algebra, 220(2) (2016), 810-821.
  • E. Houston, A. Mimouni and M. H. Park, Star operations on overrings of Prufer domains, Comm. Algebra, 45(8) (2017), 3297-3309.
  • E. G. Houston and M. H. Park, A characterization of local Noetherian domains which admit only nitely many star operations: The in nite residue eld case, J. Algebra, 407 (2014), 105-134.
  • J. Jager, Langenberechnung und kanonische Ideale in eindimensionalen Ringen, Arch. Math. (Basel), 29(5) (1977), 504-512.
  • E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc., 25 (1970), 748-751.
  • E. Kunz, Beispiel: Die kanonische Idealklasse eines eindimensionalen Cohen- Macaulay-Rings, 103, Lecture Notes in Math., Vol. 238, Springer, Berlin, (1971), 17-24.
  • T. Matsuoka, On the degree of singularity of one-dimensional analytically irreducible Noetherian local rings, J. Math. Kyoto Univ., 11 (1971), 485-494.
  • J. C. Rosales and P. A. Garca-Sanchez, Numerical Semigroups, Developments in Mathematics, 20, Springer, New York, 2009.
  • D. Spirito, Star operations on numerical semigroups, Comm. Algebra, 43(7) (2015), 2943-2963.
  • B. White, Star Operations and Numerical Semigroup Rings, Ph.D. thesis, The University of New Mexico, 2014.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Dario Spirito Bu kişi benim

Yayımlanma Tarihi 8 Ocak 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Spirito, D. (2019). STAR OPERATIONS ON KUNZ DOMAINS. International Electronic Journal of Algebra, 25(25), 171-185. https://doi.org/10.24330/ieja.504142
AMA Spirito D. STAR OPERATIONS ON KUNZ DOMAINS. IEJA. Ocak 2019;25(25):171-185. doi:10.24330/ieja.504142
Chicago Spirito, Dario. “STAR OPERATIONS ON KUNZ DOMAINS”. International Electronic Journal of Algebra 25, sy. 25 (Ocak 2019): 171-85. https://doi.org/10.24330/ieja.504142.
EndNote Spirito D (01 Ocak 2019) STAR OPERATIONS ON KUNZ DOMAINS. International Electronic Journal of Algebra 25 25 171–185.
IEEE D. Spirito, “STAR OPERATIONS ON KUNZ DOMAINS”, IEJA, c. 25, sy. 25, ss. 171–185, 2019, doi: 10.24330/ieja.504142.
ISNAD Spirito, Dario. “STAR OPERATIONS ON KUNZ DOMAINS”. International Electronic Journal of Algebra 25/25 (Ocak 2019), 171-185. https://doi.org/10.24330/ieja.504142.
JAMA Spirito D. STAR OPERATIONS ON KUNZ DOMAINS. IEJA. 2019;25:171–185.
MLA Spirito, Dario. “STAR OPERATIONS ON KUNZ DOMAINS”. International Electronic Journal of Algebra, c. 25, sy. 25, 2019, ss. 171-85, doi:10.24330/ieja.504142.
Vancouver Spirito D. STAR OPERATIONS ON KUNZ DOMAINS. IEJA. 2019;25(25):171-85.