Vol. 51, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
On separable polynomials over a commutative ring

Frank Rimi DeMeyer

Vol. 51 (1974), No. 1, 57–66
Abstract

Separable polynomials over an arbitrary commutative ring are studied. Given any separable polynomial p(X) over the commutative ring R one can find a “splitting ring” for p(X) which is a finitely generated normal separable extension of R generated by roots of p(X). A polynomial closure Λ of R generated by roots of separable polynomials is constructed. Any separable polynomial over Λ factors into linear factors in Λ. A Galois theory for such extensions is discussed. Applications to separable extensions of von Neumann regular rings and the Brauer group are given.

Mathematical Subject Classification 2000
Primary: 13B25
Milestones
Received: 8 November 1972
Published: 1 March 1974
Authors
Frank Rimi DeMeyer