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On algebra with universal finite module of differentials

Published online by Cambridge University Press:  22 January 2016

Norio Yamauchi
Norio Yamauchi*
Affiliation:
Shotoku-Gakuen Women’s Junior College
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Let k be a field and A a noetherian k-algebra. In this note, we shall study the universal finite module of differentials of A over k, which is denoted by Dk(A). When the characteristic of k is zero, detailed results have been obtained by Scheja and Storch [8]. So we shall treat the positive characteristic case. In § 1, we shall study differential modules of a local ring over subfields. We obtain a criterion of regularity (Theorem (1.14)). In § 2, we shall study the formal fibres and regular locus of A with Dk(A). Our main result is Theorem (2.1) which shows that, if Dk(A) exists, then A is a universally catenary G-ring under a certain assumption. In the local case, this is a generalization of Matsumura’s theorem ([5] Theorem 15), where regularity of A is assumed.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 83 , October 1981 , pp. 107 - 121
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

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