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Note on multiplicities of ideals. (English) Zbl 0192.13901


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[1] Geddes, A., A short proof of the existence of coefficient fields for complete, equicharacteristic local rings. J. London Math. Soc.29 (1954), 334–341. · Zbl 0056.02904 · doi:10.1112/jlms/s1-29.3.334
[2] Lech, C., On the associativity formula for multiplicities. Ark. Math.3 (1958), 301–314 (1956). · Zbl 0089.26002 · doi:10.1007/BF02589424
[3] Nagata, M., Some remarks on local rings. Nagoya Math. J.6 (1953), 53–58. · Zbl 0053.01802
[4] –, The theory of multiplicity in general local rings. Proceedings of the international symposium on algebraic number theory. Tokyo-Nikko, 1955, pp. 191–226. Science Council of Japan, Tokyo, 1956.
[5] Northcott, D. G., Ideal theory. Cambridge Tracts in Math. and Math. Phys.42. Cambridge 1953, 111 pp. · Zbl 0052.26801
[6] –, Semi-regular local rings. Mathematika3 (1956), 117–126. · Zbl 0074.02801 · doi:10.1112/S0025579300001789
[7] Northcott, D. G. andRees, D., Reductions of ideals in local rings. Proc. Cambridge Phil. Soc.50 (1954), 145–158. · Zbl 0057.02601 · doi:10.1017/S0305004100029194
[8] Rees, D., The grade of an ideal or module. Proc. Cambridge Phil. Soc.53 (1957), 28–42. · Zbl 0079.26602 · doi:10.1017/S0305004100031960
[9] Samuel, P., Algebre locale, Mémorial Sci. Math. 123. Paris 1953, 76 pp.
[10] Serre, J.-P., Géométrie algébrique et géométrie analytique. Ann. Inst. Fourier, Grenoble6 (1955–1956), 1–42.
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