  In this paper, we define and discuss higher-dimensional and absolute versions
of symmetric, Frobenius, and quasi-Frobenius algebras. In particular, we
compare these with the relative notions defined by Scheja and Storch. We also
prove the validity of codimension two-argument for modules over a coherent
sheaf of algebras with a $2$-canonical module, generalizing a result of the
author.
