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We study the generation of the Frobenius algebra of the injective
hull of a complete Stanley–Reisner ring over a field with positive
characteristic. In particular, by extending the ideas used by
M. Katzman to give a counterexample to a question raised by
G. Lyubeznik and K.E. Smith about the finite generation of Frobenius
algebras, we prove that the Frobenius algebra of the injective
hull of a complete Stanley–Reisner ring can be only principally
generated or infinitely generated. Also, by using our explicit description
of the generators of such algebra and applying the recent
work by M. Blickle about Cartier algebras and generalized test ideals,
we are able to show that the set of F -jumping numbers of
generalized test ideals associated to complete Stanley–Reisner rings
form a discrete subset inside the non-negative real numbers.
CitacióAlvarez, J.; Boix, A.F.; Zarzuela, S. Frobenius and Cartier algebras of Stanley-Reisner rings. "Journal of algebra", 15 Maig 2011, vol. 358, p. 162-177.