Regular representations of semisimple algebras, separable field extensions, group characters, generalized circulants, and generalized cyclic codes (Q1805200)

Let \(A\) be a semisimple, \(n\)-dimensional, commutative algebra over a field. The author gives an elementary proof that such an algebra over an infinite field is generated by a single element. Moreover he describes the subalgebras of \(A\) in terms of certain partitions of the set \(\{1,2, 3,\dots, n\}\). The main part of the paper is dealing with applications of these concepts to domains indicated in the title.