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THE NUMBER OF ROOTS OF A POLYNOMIAL SYSTEM

Published online by Cambridge University Press:  09 November 2020

NGUYEN CONG MINH
Affiliation:
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam e-mail: minhnc@hnue.edu.vn
LUU BA THANG
Affiliation:
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam
TRAN NAM TRUNG
Affiliation:
Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam and TIMAS, Thang Long University, Hanoi, Vietnam e-mail: tntrung@math.ac.vn
Corresponding

Abstract

Let I be a zero-dimensional ideal in the polynomial ring $K[x_1,\ldots ,x_n]$ over a field K. We give a bound for the number of roots of I in $K^n$ counted with combinatorial multiplicity. As a consequence, we give a proof of Alon’s combinatorial Nullstellensatz.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The third author is partially supported by NAFOSTED (Vietnam), grant number 101.04–2018.307.

References

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