Finite complete intersection algebras and the completeness radical

[摘要] Let A be a ring. and let B be a finite A-algebra. If B is of the form A[X-1,..., X-n](f(1),..., f(n)) then we say that B is a complete intersection over A. We show that such an algebra is projective as an A-module and Gorenstein as an A-algebra. Under the condition that A is noetherian we show that the finite A-algebras of the form A[[X-1,..., X-m]]/(g(1),..., g(m)) are exactly those complete Intersections B over A for which one has B = A.1 + root cr(A).B. Here cr(A) denotes the largest ideal of A with respect to which A is complete. This ideal, which we call the completeness radical of A, satisfies the usual radical axioms. (C) 1997 Academic Press.

[发布日期] 1997-10-15