Free duals and regular sequences (Q802675)

Let R be a local Noetherian ring. The author states some conditions in terms of the first Koszul homology for its ideals to be generated by a regular sequence. Then an analogous problem for conormal modules is considered and some evidence for the conjecture of \textit{W. V. Vasconcelos} [J. Pure Appl. Algebra 38, 367-378 (1985; Zbl 0574.13013)] are developed. Finally a condition, by means of Hochschild cohomology, for a locally complete intersection algebra to be regular is given.