Reflexive equivalence and reflexive-minimal algebras

Comment

Two algebras are reflexively equivalent if their categories of reflexive modules are equivalent. We prove that every finite-dimensional algebra has a unique basic reflexive-minimal algebra, up to isomorphism, and compute it explicitly. We extend these results to module-finite algebras over henselian local rings of dimension at most one under a dominant dimension condition at minimal primes.

We also introduce reflexive modules over additive categories and prove that taking reflexive modules is idempotent. As an application, we classify reflexive equivalence classes of algebras with finitely many indecomposable reflexive modules.