Self-duality and ring extensions
The author studies the relationship between ring extensions and self- duality. He generalizes a result of Fuller and Haack (a finite 'zR semigroup ring' over a ring with self-duality has itself a self-duality) in the following Theorem: Let \(A\supseteq B\) be a ring extension. If A has a finite free basis over B each member of which centralizes all the elements of B, B has a self-duality induced by \({}_ BV_ B\), and if the structure constants of A with respect to the above basis commute with each element of V, then A has a self-duality induced by \(_ AHom_ B(_ BA_ A,_ BV).\)
scientific article; zbMATH DE number 3853303