Let R = K[x1,⋯,xn] be a
polynomial ring, where K is a field of characteristic zero, and embed R in the
polynomial ring S = K[yij: 1 ≦ i ≦ n − 1,1 ≦ j ≦ n] by mapping xj to the
minor of the matrix [yij] obtained by deleting the j-th column. Let I be a
homogeneous radical ideal of R. It will be shown that if IS is radical, then I is
semiregular, that is, R∕I is Cohen-Macaulay. Several other related results will be
eslablished, in which the fact that certain expanded radical ideals remain
radicaI either implies, or is implied by, the fact that certain other ideals are
semiregular. Each one of these results has some connection with invariant
theory.
