CONTRACTED, $\mathfrak{m}$-FULL AND RELATED CLASSES OF IDEALS IN LOCAL RINGS
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 669-675

Voir la notice de l'article provenant de la source Cambridge University Press

The class of $\mathfrak{m}$-full and four related classes of ideals in a local ring (R, $\mathfrak{m}$) are extended by replacing $\mathfrak{m}$ with other ideals and the resulting classes of ideals are compared. It is shown that contracted ideals are $\mathfrak{m}$-full in a local ring with infinite residue field.
DOI : 10.1017/S0017089512000833
Mots-clés : 13H99, 13E05, 13B22
RUSH, DAVID E. CONTRACTED, $\mathfrak{m}$-FULL AND RELATED CLASSES OF IDEALS IN LOCAL RINGS. Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 669-675. doi: 10.1017/S0017089512000833
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[1] 1.Conca, A., De Negri, E. and Rossi, M. E., Integrally closed and componentwise linear ideals, Math. Z. 265 (2010), 715–734. Google Scholar | DOI

[2] 2.D'Cruz, C., Quadratic transform of complete ideals in regular local rings, Commun. Algebra 28 (2000), 693–698. Google Scholar

[3] 3.Epstein, N., A guide to closure operations in commutative algebra, in Progress in commutative algebra 2 (Walter de Gruyter, Berlin, 2012), 1–37. Google Scholar

[4] 4.Goto, S., Integral closedness of complete–intersection ideals, J. Algebra 108 (1987), 151–160. Google Scholar | DOI

[5] 5.Heinzer, W., Lantz, D. and Shah, K., The Ratliff–Rush ideals in a Noetherian ring, Commun. Algebra 20 (1992), 591–622. Google Scholar

[6] 6.Heinzer, W., Ratliff, L. J. Jr. and Rush, D. E., Basically full ideals in local rings, J. Algebra 250 (2002), 371–396. Google Scholar | DOI

[7] 7.Hong, J., Lee, H., Noh, S. and Rush, D. E., Full ideals, Commun. Algebra 37 (2009), 2627–2639. Google Scholar | DOI

[8] 8.Huneke, C., Complete ideals in two-dimensional regular local rings, Proceedings of the Microprogram in Commutative Algebra, MSRI, Berkeley (1987), Springer, New York (1989), 325–338. Google Scholar

[9] 9.Matsumura, H., Commutative ring theory (Cambridge University Press, Cambridge, UK, 1986). Google Scholar

[10] 10.Petro, J. W., Some results on the asymptotic completion of an ideal, Proc. Amer. Math. Soc. 15 (1964), 519–524. Google Scholar | DOI

[11] 11.Ratliff, L. J. Jr., Δ-closures of ideals and rings, Trans. Amer. Math. Soc. 313 (1) (1989), 221–247. Google Scholar

[12] 12.Ratliff, L. J. Jr. and Rush, D. E., Asymptotic primes of Delta-closures of ideals, Commun. Algebra 30 (1) (2002), 1513–1531. Google Scholar

[13] 13.Sakuma, M., On prime operations in the theory of ideals, Hiroshima Math. J. 20 (1957), 101–106. Google Scholar | DOI

[14] 14.Swanson, I. and Huneke, C., Integral closure of ideals, rings, and modules, London Math. Soc. Lecture Note Series 336 (Cambridge University Press, Cambridge, UK, 2006). Google Scholar

[15] 15.Vasconcelos, W., Integral closure, Rees algebras, multiplicity and algorithms (Springer, New York, 2005). Google Scholar

[16] 16.Vassilev, J., Structure on the set of closure operations on a commutative ring, J. Algebra 321 (2009), 2737–2753. Google Scholar | DOI

[17] 17.Vassilev, J. and Vraciu, A., When is the tight closure determined by the test ideal?, J. Commutative Algebra 1 (2009), 591–602. Google Scholar | DOI

[18] 18.Watanabe, J., -full ideals, Nagoya Math. J. 106 (1987), 101–111. Google Scholar

[19] 19.Yao, Y., Modules with finite F-representation type, J. London Math. Soc. 72 (2005), 53–72. Google Scholar | DOI

[20] 20.Zariski, O. and Samuel, P., Commutative algebra, Vol. II (D. Van Nostrand, New York, 1960). Google Scholar | DOI

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