Derivations into the integral closure
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- by Richard Draper and Klaus Fischer PDF
- Trans. Amer. Math. Soc. 271 (1982), 283-298 Request permission
Abstract:
Let $A$ be a reduced analytical $k$-algebra of dimension $r$ and $A’$ its integral closure in the full ring of quotients of $A$. We investigate the condition on $A$ that there exist $r$ elements ${x_1}, \ldots ,{x_r}$ in $A$ and $k$-derivations ${d_1}, \ldots ,{d_r}$ from $A$ into $A’$ so that ${d_i}({x_j})$ is the $r \times r$ identity matrix and so that ${d_1}, \ldots ,{d_r}$ freely generate ${\operatorname {Der} _k}(A, A’ )$. We show this is equivalent to a number of other conditions. If $A$ is a complete intersection, then the above is equivalent to the Jacobian ideal $J$ becoming principal in $A’$. If $A / \sqrt J$ is regular of dimension $r - 1$ and satisfies the above condition, then $A’$ is regular.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 271 (1982), 283-298
- MSC: Primary 32B05; Secondary 13B10, 13B20, 32B30
- DOI: https://doi.org/10.1090/S0002-9947-1982-0648093-4
- MathSciNet review: 648093