Journal of Commutative Algebra

Decompositions of ideals into irreducible ideals in numerical semigroups

Valentina Barucci

Full-text: Open access

Article information

Source
J. Commut. Algebra, Volume 2, Number 3 (2010), 281-294.

Dates
First available in Project Euclid: 18 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.jca/1287409178

Digital Object Identifier
doi:10.1216/JCA-2010-2-3-281

Mathematical Reviews number (MathSciNet)
MR2728145

Zentralblatt MATH identifier
1237.20056

Citation

Barucci, Valentina. Decompositions of ideals into irreducible ideals in numerical semigroups. J. Commut. Algebra 2 (2010), no. 3, 281--294. doi:10.1216/JCA-2010-2-3-281. https://projecteuclid.org/euclid.jca/1287409178


Export citation

References

  • V. Barucci, On propinquity of numerical semigroups and one-dimensional local Cohen-Macaulay rings, in Commutative algebra and its applications, M. Fontana, S. Kabbaj, O. Olberding and I. Swanson, eds., de Gruyter, Berlin, 2009%, 49–60.
  • V. Barucci, Local rings of minimal length, J. Pure Appl. Algebra 213 (2009), 991-996.
  • ––––, Numerical semigroup algebras, in Multiplicative ideal theory in commutative algebra, J.W. Brewer, S. Glaz, H. Heinzer and B. Olberding, eds., Springer, Berlin, 2006%, 39–53.
  • R. Fröberg, C. Gottlieb and R. Häggkvist, Semigroups, semigroup rings and analytically irreducible rings, Reports Dept. Math. Univ. Stockholm 1, 1986.
  • L. Fuchs, W. Heinzer and B. Olberding, Commutative ideal theory without finiteness conditions: irreducibility in the quotient field, in Abelian groups, rings, modules, and homological algebra, Lect. Notes Pure Appl. Math. 249, Chapman and Hall/CRC, Boca Raton, FL, 2006%, 121–145.
  • C. Gottlieb, On generarors of ideals in one-dimensional local rings, Comm. Algebra 21 (1993), 421-425.
  • W. Heinzer, J. Huckaba and I. Papick, $m$-canonical ideals in integral domains, Comm. Algebra 26 (1998), 3021-3043.
  • E. Noether, Idealtheorie in Ringbereichen, Math. Ann. 83 (1921), 24-66.
  • J.C. Rosales, P.A. García-Sanchez and J.I. García-García, Irreducible ideals of finitely generated commutative monoids, J. Algebra 238 (2001), 328-344.