Vol. 52, No. 2, 1974

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Some remarks on high order derivations

Yasunori Ishibashi

Vol. 52 (1974), No. 2, 419–424

Let k, A and B be commutative rings such that A and B are k-algebras. In this paper it is shown that Ωk(q)(AkB), the module of high order differentials of A kB can be expressed by making use of Ωk(i)(A) and Ωk(j)(B). On the other hand let K∕k be a finite purely inseparable field extension. Sandra Z. Keith has given a criterion for a k-linear mapping of K into itself to be a high order derivation of K∕k. The representation of Ωk(q)(A kB) is used to show that Keith’s result is valid for larger class of algebras.

Mathematical Subject Classification 2000
Primary: 13B10
Received: 1 August 1973
Published: 1 June 1974
Yasunori Ishibashi