Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fields of constants of infinite higher derivations


Author: James K. Deveney
Journal: Proc. Amer. Math. Soc. 41 (1973), 394-398
MSC: Primary 12F10; Secondary 12F15
MathSciNet review: 0335478
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ K$ be a field of characteristic $ p \ne 0$, and let $ P$ be its maximal perfect subfield. Let $ h$ be a subfield of $ K$ containing $ P$ such that $ K$ is separable over $ h$. We prove: Every regular subfield of $ K$ containing $ h$ is the field of constants of a set of higher derivations on $ K$ if and only if (1) the transcendence degree of $ K$ over $ h$ is finite, and (2) $ K$ has a separating transcendency basis over $ h$. This result leads to a generalization of the Galois theory developed in [4].


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12F10, 12F15

Retrieve articles in all journals with MSC: 12F10, 12F15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0335478-9
PII: S 0002-9939(1973)0335478-9
Keywords: Higher derivation, regular extension field
Article copyright: © Copyright 1973 American Mathematical Society