Effective Genericity, Delta-Regularity and Strong Noether Position

Reference: Communications in Algebra, 40 (2012) 3933-3949

Description: It is shown that the concept of strong Noether position for a polynomial ideal recently introduced by Hashemi is equivalent to delta-regularity and thus related to Pommaret bases. In particular, I provide explicit Pommaret bases for two of the ideal sequences used by him for the definition of strong Noether position and alternative proofs for a number of his statements. Finally, I show that one consequence of delta-regularity is that any Pommaret basis contains a system of parameters and I present an algorithm for checking whether the factor ring is Gorenstein via a socle computation.

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