Colength of derivation ideals
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- by Kenneth Kramer PDF
- Proc. Amer. Math. Soc. 40 (1973), 346-350 Request permission
Abstract:
In this paper, $D$ is a derivation acting on the formal power series ring $K[[{t_1}, \cdots ,{t_r}]]$ over a field $K$ of characteristic $p \ne 0$. We conjecture that the colengths of the ideals ($({D^{{p^n}}}{t_1}, \cdots ,{D^{{p^n}}}{t_r})$ and $({D^{{p^{n - 1}}}}{t_1}, \cdots ,{D^{{p^{n - 1}}}}{t_r})$ are congruent modulo ${p^n}$, provided they are finite. We give a proof for the case $r = 1$ and any $n \geqq 1$, and for the case $n = 1$ and any $r \geqq 1$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 346-350
- MSC: Primary 13B10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318122-6
- MathSciNet review: 0318122