Correction to on the Brauer Group of Algebras Having a Grading and an Action

Orzech, Morris

Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1523-1524

Résumé

Let R be a commutative ring, G a finite abelian group. Let A be an R-algebra which is graded by G (i.e. A = Σ⊕σ∈G A σ , where AσAτ ⊂ Aστ for σ, τ in G) and for which A1 is an R-module of finite type. In Remark 4.1 (a) of [1] we asserted that under these hypotheses if u is in A and u + pA is homogeneous in A/pA for each maximal ideal p of R then u is homogeneous in A. We used this assertion for u a unit in A such that a → uau–1 is a grading-preserving homomorphism. K. Ulbrich has kindly pointed out a counterexample to the assertion: R = Z/4Z, G = {1, σ};, u = 2σ + 1, p = 2R. Proposition 4.2 of [1] uses the erroneous result and is in turn invoked later in the paper.

Détail

DOI : 10.4153/CJM-1980-121-3

Bibliographie

[1] 1. Orzech, M., On the Brauer group of algebras having a grading and an action, Can. J. Math. 28 (1976), 533–552. Google Scholar