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Blow Up Sequences and the Module of nth Order Differentials

Published online by Cambridge University Press:  20 November 2018

William C. Brown
William C. Brown*
Affiliation:
Michigan State University, East Lansing, Michigan
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Let C denote an irreducible, algebraic curve defined over an algebraically closed field k. Let ? be a singular point of C. We shall employ the following notation throughout the rest of this paper: R will denote the local ring at P, K the quotient field of the integral closure of R in K, A the completion of R with respect to its radical topology, and Ā the integral closure of A in its total quotient ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1289 - 1301
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Auslander, M. and Buchsbaum, D. A., On ramification theory in noetherian rings, Amer. J. Math. 81 (1959), 749–765.Google Scholar
2. DeMeyer, F. and Ingraham, E., Separable algebras over commutative rings, Lecture Notes in Mathematics 181 (Springer-Verlag, 1971).Google Scholar
3. Fischer, K., The module decomposition 1(1/'A), Trans. Amer. Math. Soc. 186 (1973), 113–128.Google Scholar
4. Lipman, J., Stable ideals and Arf rings, Amer. J. Math. 93 (1971), 649–685.Google Scholar
5. Mount, K. and Villamayor, O. E., Taylor series and higher derivations, Departmento de Mathematicas Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires, Série No. 18, Buenos Aires, 1969.Google Scholar
6. Nagata, M., Local rings (Interscience, 1969).Google Scholar
7. Nakai, Y., Higher order derivations I, Osaka J. Math. 7 (1970), 1–27.Google Scholar
8. Sanders, D., Epimorphisms and subalgebras of finitely generated algebras, Thesis, Michigan State University.Google Scholar
9. Zariski, O. and Samuel, P., Commutative algebra, Vol. II. (D. Van Nostrand, Princeton, 1960).Google Scholar