Cancellative semigroup rings which are Azumaya algebras
A very satisfactory characterization of group rings which are Azumaya algebras has been obtained by \textit{F. DeMeyer} and \textit{G. Janusz} [Trans. Am. Math. Soc. 279, 389-395 (1983; Zbl 0525.16002)]. Let S be a cancellative semigroup, U(S) its group of units and G the two-sided group of fractions of S. The authors reduce the problem of characterizing semigroup rings K[S] which are Azumaya algebras to a problem about K[U(S)] and the tools used in this characterization are exactly the relations between K[U(S)], K[S] and K[G]. As a by-product of their results are obtained a new class of examples of Azumaya algebras that do not arise in a more trivial way.
scientific article; zbMATH DE number 4075406