Exercise 6, § 20

Let K be a commutative field. We say that a K-algebra A is symmetric if it admits a tracial invertible linear form (VIII, p. 115, Exercise 3).

a) Prove that a symmetric algebra has finite degree and is Frobenius.

b) Prove that the algebra of a finite group over K is symmetric.

c) A semisimple algebra of finite degree over K is symmetric.