# Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## Higher derivations on finitely generated integral domains. IIHTML articles powered by AMS MathViewer

by William C. Brown
Proc. Amer. Math. Soc. 51 (1975), 8-14 Request permission

## Abstract:

We prove Theorem. Let $A = k[{x_1}, \ldots ,{x_m}]$ be a finitely generated integral domain over a field $k$ of characteristic zero. Then $A$ regular, i.e. the local ring ${A_q}$ is regular for every prime ideal $q \subseteq A$, is equivalent to the following two conditions: (1) no prime of $A$ of height greater than one is differential, and (2) for all $\phi \in {\operatorname {Hom} _k}(A,A),\phi \in \operatorname {Der} _k^n(A)$ if and only if $\Delta \phi \in \Sigma _{i = 1}^{n - 1}\operatorname {Der} _k^i(A) \cup \operatorname {Der} _k^{n - i}(A)(n = 1,2, \ldots )$. Here $\Delta$ denotes the Hochschild coboundary operator, $\cup$ denotes the cup product, and $\operatorname {Der} _k^n(R)$ is the module of higher derivations of rank $n$.
Similar Articles
• Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13B10
• Retrieve articles in all journals with MSC: 13B10