An ideal separating extension of affine space

Pedersen, Paul

doi:10.1090/S0002-9947-07-04123-2

An ideal separating extension of affine space
HTML articles powered by AMS MathViewer

by Paul S. Pedersen PDF

Trans. Amer. Math. Soc. 359 (2007), 3071-3083 Request permission

Abstract:

In affine space the set of solutions to a system of polynomial equations does not uniquely determine the system. We extend affine space so that the solutions (in the extension) to a system of equations uniquely determines the system.

References

F. S. Macaulay, The algebraic theory of modular systems, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1994. Revised reprint of the 1916 original; With an introduction by Paul Roberts. MR 1281612
Paul S. Pedersen, Basis for power series solutions to systems of linear, constant coefficient partial differential equations, Adv. Math. 141 (1999), no. 1, 155–166. MR 1667149, DOI 10.1006/aima.1998.1782
David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
David Cox, John Little, and Donal O’Shea, Ideals, varieties, and algorithms, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1992. An introduction to computational algebraic geometry and commutative algebra. MR 1189133, DOI 10.1007/978-1-4757-2181-2
M. G. Marinari, H. M. Möller, and T. Mora, On multiplicities in polynomial system solving, Trans. Amer. Math. Soc. 348 (1996), no. 8, 3283–3321. MR 1360228, DOI 10.1090/S0002-9947-96-01671-6