The strong Brauer group of a cocommutative coalgebra (Q1612107)

The Brauer group of a cocommutative coalgebra was introduced by \textit{Y. H. Zhang}, the second author and the reviewer [in J. Algebra 177, No. 2, 536-568 (1995; Zbl 0837.16037)]. Using strong equivalences, as introduced by \textit{B. I. Lin} [Commun. Algebra 1, 311-344 (1974; Zbl 0285.16021)], instead of Morita-Takeuchi equivalences the authors define and study a new subgroup, the strong Brauer group, of the mentioned Brauer group of a coalgebra. It is shown that the strong Brauer group embeds in the usual Brauer group of the convolution algebra of the coalgebra and therefore it is torsion. Some cases when the two Brauer groups coincide are considered.