A question of Guralnick about reflexive algebras Original Research Article

Let A be a commutative, finite-dimensional, local k-algebra, and set B = EndA(M), where M is a finitely generated, faithful, indecomposable A-module. Guralnick asked whether B must equal A if B is an intermediate algebra of A, i.e., if the A- and B-submodules of M are the same. We give a class of examples where this is not the case.