Normal Rees algebras

On the depth of blowup algebras of ideals with analytic deviation one

“…We also show that if / is an ideal which verifies the hypothesis of Theorem 3.1, then the Rees algebra R(I) satisfies Serre's property S2, when A/I satisfies Si (Theorem 4.4). The corresponding result for almost complete intersections has been proved by P. Brumatti, A. Simis, and W. V. Vasconcelos in [1].…”

Remarks on a remark of Kaplansky

“…It is interesting to note, that Brumatti, Simis and Vasconcelos have found the equality I i)J = (Ix , J(x -1 )) n R to be useful in certain computations in computer algebra [2]. Lemma 2.1.…”

Integrally closed almost complete intersection ideals

“…The ideals described in Theorem 4.2 are not necessarily normal. In fact, for a hypersurface ring, in [2], there are necessary and sufficient conditions for the maximal ideal m to be normal.…”

“…Note that A is a one-dimensional CohenMacaulay domain, e(A) = 2 and m 2 = (x + y)m. Then μ(m n ) = 2 for all n 2 and, by using the algorithm described in [2], it can be checked that m is a normal ideal. On the other hand, in the ring A = CJx, yK/(y 2 ), we have e(A) = 2, m 2 = xm and the ideal K = m 2 = (x 2 , xy) is of type (2), but is not integrally closed as y ∈ K \ K.…”