Notes on kernels of rational higher derivations in integrally closed domains. (English) Zbl 1419.13049

Summary: Let \(k\) be a field of characteristic \(p \geq 0\) and \(A = k[x_0, x_1, x_2, \ldots]\) the polynomial ring in countably many variables over \(k\). We construct a rational higher \(k\)-derivation on \(A\) whose kernel is not the kernel of any higher \(k\)-derivation on \(A\). This example extends [P. Jȩdrzejewicz, Colloq. Math. 99, No. 1, 51–53 (2004; Zbl 1075.13504); Example 4].


13N10 Commutative rings of differential operators and their modules
13F20 Polynomial rings and ideals; rings of integer-valued polynomials


Zbl 1075.13504
Full Text: Euclid


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