Corrigendum: Generalizations of graded Clifford algebras and of complete intersections

Abstract

A correction is provided for Proposition 3.5 in the article “Generalizations of Graded Clifford Algebras and of Complete Intersections”. The correction is: if S is a skew polynomial ring on finitely many generators of degree one that are normal elements in S, and if I is a homogeneous ideal of S that is generated by a normalizing sequence, then dimk(S/I) is finite if and only if S/I has no point modules and no fat point modules. A similar correction is provided for Corollary 3.6 of the same article. The proof of Proposition 3.5 in [4] contains an error, so that [4, Proposition 3.5 and Corollary 3.6] need to be modified (see Proposition 10 and Corollary 11 below). The authors would like to thank J. T. Stafford for alerting them to this issue, which occurs in the paragraph in [4] immediately preceding Proposition 3.5. The main result of [4], namely Theorem 4.2, is correct as stated, provided that the definitions of base point and base-point free are changed from those given in [4, Definition 1.7] to those given in Definition 2 below. The examples and other results in the remaining sections of [4] are unchanged. Additionally, the reader should note that the results in [7] are unchanged. We recall the notation of [4]: k denotes an algebraically closed field; k = k {0} and similarly for modules and other rings; Mc(k) is the ring of c× c matrices over k; μ = (μij) ∈ Mn(k ), where μijμji = 1 for all i, j; S = k〈z1, . . . , zn〉/〈U〉, where U = span{zjzi − μijzizj : 2010 Mathematics Subject Classification: . 16S38, 16S37, 16S36.