Strong F-regularity and generating morphisms of local cohomology modules

We establish a criterion for the strong F-regularity of a (non-Gorenstein) Cohen-Macaulay reduced complete local ring of dimension at least 2, containing a perfect field of prime characteristic p. We also describe an explicit generating morphism (in the sense of Lyubeznik) for the top local cohomology module with support in certain ideals arising from an n×(n−1) matrix X of indeterminates. For p≥5, these results led us to derive a simple, new proof of the well-known fact that the generic determinantal ring defined by the maximal minors of X is strongly F-regular.