Geodesic
Integral closures of ideals relative to Artinian modules, and exact sequences
Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 103-107

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

In [3], Sharp and Taherizadeh introduced concepts of reduction and integral closure of an ideal I of a commutative ring R (with identity) relative to an Artinian R-module A, and they showed that these concepts have properties which reflect some of those of the classical concepts of reduction and integral closure introduced by Northcott and Rees in [2]. 
Sharp, R. Y.; Tiraş, Y. Integral closures of ideals relative to Artinian modules, and exact sequences. Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 103-107. doi: 10.1017/S0017089500008582
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[1] 1.Kirby, D., Artinian modules and Hilbert polynomials, Quart. J. Math. Oxford Ser. (2) 24 (1973), 47–57. Google Scholar | DOI

[2] 2.Northcott, D. G. and Rees, D., Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145–158. Google Scholar | DOI

[3] 3.Sharp, R. Y. and Taherizadeh, A.-J., Reductions and integral closures of ideals relative to an Artinian module, J. London Math. Soc. (2) 37 (1988), 203–218. Google Scholar

[4] 4.Sharp, R. Y., Tiras, Y., and Yassi, M., Integral closures of ideals relative to local cohomology modules over quasi-unmixed local rings, J. London Math. Soc. (2) 42 (1990), 385–392. Google Scholar

[5] 5.Sharpe, D. W. and Vdmos, P., Injective modules (Cambridge University Press, 1972). Google Scholar

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