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On algebra with universal finite module of differentials
| Content Provider | Scilit |
|---|---|
| Author | Yamauchi, Norio |
| Copyright Year | 1981 |
| Description | 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 $D_{k}$(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 $D_{k}$(A). Our main result is Theorem (2.1) which shows that, if $D_{k}$(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. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9797AA2F3D0F719C99A606BD1CF87B27/S0027763000019437a.pdf/div-class-title-on-algebra-with-universal-finite-module-of-differentials-div.pdf |
| Ending Page | 121 |
| Page Count | 15 |
| Starting Page | 107 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000019437 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 83 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1981-10-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Applied Mathematics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
