Vol. 34, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Characterization of separable ideals

Bryce L. Elkins

Vol. 34 (1970), No. 1, 45–49
Abstract

A k-algebra A is called separable if the exact sequence of left Ae = AkA0-modules: 0 J Ae ϕA 0 splits, where p(a b0) = a b; a two-sided ideal A of A is separable in case the k-algebra A∕A is separable.

In this note, we present two characterizations of separable ideals. In particular, one finds that a monic polynomial f k[x] generates a separable ideal if, and only if, f = g1gs, where the gi are monic polynomials which generate pairwise comaximal indecomposable ideals in k[x], and f(a) is a unit in k[a] = k[x]∕f k[x](a = x + f k[x]).

Mathematical Subject Classification
Primary: 16.20
Milestones
Received: 11 November 1969
Published: 1 July 1970
Authors
Bryce L. Elkins