Abstract :
Let R = k[x1, …, xn] and R[x] be a polynomial ring over a field k and let I be a normal ideal of R generated by square free monomials of the same degree. We prove that I + x(x1, …, xn) and I + (xx1) are both normal ideals of R[x]. The ideals It, and It + xIt − 2 are shown to be normal, where It, is the ideal of R generated by the square free monomials of degree t. Let P be the ideal of relations of the semigroup ring k[xixj ¦ 1 ≤ i < j ≤ n]. We prove that the toric ideal P has a quadratic reduced Gröbner basis with respect to a lexicographical ordering, then we uncover some classes of Cohen-Macaulay rings and compute their Hubert series.
