Some remarks on high order derivations

Yasunori Ishibashi

Vol. 52 (1974), No. 2, 419–424

DOI: 10.2140/pjm.1974.52.419

Abstract

Let k, A and B be commutative rings such that A and B are k-algebras. In this paper it is shown that Ω_k^(q)(A⊗_kB), the module of high order differentials of A ⊗_kB can be expressed by making use of Ω_k⁽ⁱ⁾(A) and Ω_k^(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 Ω_k^(q)(A ⊗_kB) is used to show that Keith’s result is valid for larger class of algebras.

Mathematical Subject Classification 2000

Primary: 13B10

Milestones

Received: 1 August 1973

Published: 1 June 1974