Remarks on rings of constants of derivations
HTML articles powered by AMS MathViewer
- by Wei Li PDF
- Proc. Amer. Math. Soc. 107 (1989), 337-340 Request permission
Abstract:
Let $k$ be a field of characteristic $p > 0$ and $D \ne 0$ a family of $k$-derivations of $k[x,y]$. We prove that $k{[x,y]^D}$ ,the ring of constants with respect to $D$, is a free $k[{x^p},{y^p}]$-module of rank $p$ or 1 and $k{[x,y]^D} = k[{x^p},{y^p},{f_1}, \ldots ,{f_{p - 1}}]$ for some ${f_1}, \ldots ,{f_{p - 1}} \in k{[x,y]^D}$.References
- T. Y. Lam, Serreโs conjecture, Lecture Notes in Mathematics, Vol. 635, Springer-Verlag, Berlin-New York, 1978. MR 0485842
- Hideyuki Matsumura, Commutative algebra, 2nd ed., Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. MR 575344
- Andrzej Nowicki and Masayoshi Nagata, Rings of constants for $k$-derivations in $k[x_1,\cdots ,x_n]$, J. Math. Kyoto Univ. 28 (1988), no.ย 1, 111โ118. MR 929212, DOI 10.1215/kjm/1250520561
- C. S. Seshadri, Triviality of vector bundles over the affine space $K^{2}$, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 456โ458. MR 102527, DOI 10.1073/pnas.44.5.456
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 337-340
- MSC: Primary 13N05; Secondary 12H05, 13B10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0979220-9
- MathSciNet review: 979220