Journal of Commutative Algebra

Integral closure and other operations on monomial ideals

Veronica Crispin Quiñonez

Article information

Source
J. Commut. Algebra, Volume 2, Number 3 (2010), 359-386.

Dates
First available in Project Euclid: 18 October 2010

https://projecteuclid.org/euclid.jca/1287409181

Digital Object Identifier
doi:10.1216/JCA-2010-2-3-359

Mathematical Reviews number (MathSciNet)
MR2728148

Zentralblatt MATH identifier
1238.13005

Citation

Quiñonez, Veronica Crispin. Integral closure and other operations on monomial ideals. J. Commut. Algebra 2 (2010), no. 3, 359--386. doi:10.1216/JCA-2010-2-3-359. https://projecteuclid.org/euclid.jca/1287409181

References

• V. Crispin Quiñonez, Integrally closed monomial ideals and powers of ideals, Research Reports 7, Department of Mathematics, Stockholm University, 2002. Available at http://www2.math.su.se/reports/2002/7/2002-7.pdf
• ––––, Integral closure and related operations on monomial ideals, Doctoral thesis, Stockholm University, 2006.
• S.D. Cutkosky, On unique and almost unique factorization of complete ideals, Amer. J. Math. 111 (1989), 417-433.
• ––––, On unique and almost unique factorization of complete ideals. II, Invent. Math. 98 (1989), 59-74.
• C. Huneke, The primary components of and integral closures of ideals in $3$-dimensional regular local rings, Math. Ann. 275 (1986), 617-635.
• C. Huneke, Complete ideals in two-dimensional regular local rings, Commutative algebra, (Berkeley, CA, 1987), 325-338, Math. Sci. Res. Inst. Publ. 15, Springer, New York, 1989.
• C. Huneke and J.D. Sally, Birational extension in dimension two and integrally closed ideals, L. Algebra 115 (1988), 481-500.
• C. Huneke and I. Swanson, Integral closure of ideals, rings, and modules, London Math. Soc. Lect. Note Series 336, Cambridge University Press, Cambridge, 2006.
• M. Kim, Product of distinct simple integrally closed ideals in two-dimensional regular local rings, Proc. Amer. Math. Soc. 125 (1997), 315-321.
• J. Lipman, Rational singularities, with applications to algebraic surfaces and unique factorization, Inst. Hautes Ètudes Sci. Publ. Math. 36 (1969), 195-279.
• R. Villarreal, Monomial algebras, Marcel Dekker, Inc., New York, 2001.
• K. Watanabe, Chains of integrally closed ideals, Commutative algebra (Grenoble/Lyon, 2001), 353-358, Contemp. Math. 331, American Mathematical Society, Providence, RI, 2003.
• O. Zariski, Polynomial ideals defined by infinitely near base points, Amer. J. Math. 60 (1938), 151-204.
• O. Zariski and P. Samuel, Commutative algebra, Vol. 2, D. Van Nostrand Co., Inc., Princeton, 1960.