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m-full ideals

Published online by Cambridge University Press:  22 January 2016

Junzo Watanabe
Junzo Watanabe*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya 464, Japan
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An ideal a of a local ring (R, m) is called m-full if am: y = a for some y in a certain faithfully flat extension of R. The definition is due to Rees (unpublished) and he had obtained some elementary results (also unpublished). The present paper concerns some basic properties of m-full ideals. One result is the characterization of m-fullness in terms of the minimal number of generators of ideal, generalizing his result in a low dimensional case (Theorem 2, § 2).

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 101 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Burch, L., On ideals of finite homological dimension, Proc. Cam. Phil. Soc, 64 (1968), 941–946.CrossRefGoogle Scholar
[ 2 ] Zariski, O. and Sammuel, P., Commutative Algebra II, Van Nostrand, New York, 1960.Google Scholar
[ 3 ] Rademacher, H. and Grosswald, E., Dedekind sums, Carus Math. Monog. 16, A.M.S., 1972.Google Scholar
[ 4 ] Watanabe, J., The Dilworth number of Artinian local rings and finite posets with rank function, Proceedings of Conference on Commutative Algebra and Combinatorics, Kyoto 1985, Kinokuniya Co. and North-Holland Publ. Co.Google Scholar