Complements to a paper of P. Dubreil (Q921069)

In [Bull. Soc. Math. Fr. 61, 258-283 (1933; Zbl 0008.12903)], \textit{P. Dubreil} proved estimates on the minimal number of generators of certain homogeneous ideals. For a homogeneous perfect ideal of height two this is generalized by the author, \textit{A. V. Geramita} and \textit{P. Maroscia} [Bull. Sci. Math., II. Ser. 108, 143-185 (1984; Zbl 0559.14034)]. In the paper under review the author gives a brief, straightforward, and elementary proof of Dubreil's theorems based on a property of the Castelnuovo function \(\Delta^ nH(R,m)\), \(n=\dim (R)\), R the coordinate ring and H(R,m) the Hilbert function. There is also an unexpected link between standard basis estimates of Dubreil and the author's splitting principle [see the author, Rend. Semin. Mat., Torino 43, 333-353 (1985; Zbl 0675.14024)].