Abstract
This note contains generalizations of two results of Abhyankar [1] which give a bound for the embedding dimension of certain local rings in terms of the multiplicity and the dimension of the ring.
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References
Abhyankar, S. S., "Local rings of high embedding dimension", Amer. J. Math. 89 (1967), 1073–1077.
Abhyankar, S. S., Resolutions of Singularities of Embedded Algebraic Surfaces, Academic Press, New York, 1966.
Nagata, M., Local Rings, Interscience, New York, 1962.
Swan, R. G., "The number of generators of a module", Math. Zeit. 102 (1967), 318–322.
Zariski, O. and Samuel, P., Commutative Algebra, vol. II, D. Van Nostrand, New York, 1960
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© 1973 Springer-Verlag
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Sally, J. (1973). On the number of generators of ideals of dimension zero. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068932
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DOI: https://doi.org/10.1007/BFb0068932
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