On the cohomology of Frobenius algebras (Q1196810)

Let \(\Lambda\) be a finitely generated free Frobenius algebra over a commutative ring \(R\). The author investigates the complete cohomology groups \(H^ \tau (\Lambda, -)\) [\textit{T. Nakayama}, Osaka Math. J. 9, 165-187 (1957; Zbl 0101.02601)], in particular their periodicity with respect to \(r\). Then, applications to the cohomology of the rings of integers in quadratic fields over the rationals \(\mathbb{Q}\) are presented.