A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Characterization of separable ideals

1970
*
Pacific Journal of Mathematics
*

A ά-algebra A is called separable if the exact sequence of left A e = A® ^-modules: 0 -^> J~> A* -+ A ~+ 0 splits, where φ(a<S)b°) = a-b; a two-sided ideal Sί of A is separable in case the Λ -algebra A/St is separable. In this note, we present two characterizations of separable ideals. In particular, one finds that a monic polynomial fe k[x] generates a separable ideal if, and only if, / = g 1 g s , where the gι are monic polynomials which generate pairwise comaximal indecomposable ideals in

doi:10.2140/pjm.1970.34.45
fatcat:nzqkna2danegdddslq4fsxy4si