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

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


The structure of inseparable field extensions

Author: William C. Waterhouse
Journal: Trans. Amer. Math. Soc. 211 (1975), 39-56
MSC: Primary 12F15
MathSciNet review: 0379454
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The goal of this paper is to introduce some structural ideas into the hitherto chaotic subject of infinite inseparable field extensions. The basic discovery is that the theory is closely related to the well-developed study of primary abelian groups. This analogy undoubtedly has implications beyond those included here. We consider only modular extensions, which are the inseparable equivalent of galois extensions. §§2 and 3 develop the theory of pure independence, basic subfields, and tensor products of simple extensions. The following sections are devoted to Ulm invariants and their computation; the existence of nonzero invariants of arbitrary index is proved by means of a theorem which furnishes an actual connection between primary groups and inseparable fields. The final section displays some complications in the field extensions not occurring in abelian groups.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12F15

Retrieve articles in all journals with MSC: 12F15

Additional Information

PII: S 0002-9947(1975)0379454-5
Article copyright: © Copyright 1975 American Mathematical Society