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Proceedings of the American Mathematical Society

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On system of parameters, local intersection multiplicity and Bezout's theorem


Authors: Eduard Bod’a and Wolfgang Vogel
Journal: Proc. Amer. Math. Soc. 78 (1980), 1-7
MSC: Primary 14B99; Secondary 13H15
DOI: https://doi.org/10.1090/S0002-9939-1980-0548071-3
MathSciNet review: 548071
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Abstract: This paper provides effective methods for computing the local intersection multiplicity as the length of a well-defined ideal (see Theorem and Proposition 1). There are other ways of obtaining such an ideal (see [2], [9], [12], [18]) but ours is simpler because of our use of reducing systems of parameters. Applying these ideal theoretic methods we will give a new and simple proof of Bezout's Theorem (see §4). Hence this proof again provides the connection between the different viewpoints which are treated in the work of Lasker-Macaulay-Gröbner and Severi-van der Waerden-Weil concerning the multiplicity theory.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0548071-3
Keywords: Local intersection multiplicity, system of parameters, reducing system of parameters, Cohen-Macaulay rings, Buchsbaum rings and Bezout's Theorem
Article copyright: © Copyright 1980 American Mathematical Society