Vol. 44, No. 2, 1973

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Expanded radical ideals and semiregular ideals

Melvin Hochster

Vol. 44 (1973), No. 2, 553–568

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.

Mathematical Subject Classification 2000
Primary: 13A15
Received: 13 October 1971
Published: 1 February 1973
Melvin Hochster
Department of Mathematics
University of Michigan
East Hall, 530 Church Street
Ann Arbor MI 48109-1043
United States