Frobenius and Cartier algebras of Stanley–Reisner rings

Frobenius and Cartier algebras of Stanley–Reisner rings

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...

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Veröffentlicht in:Journal of algebra 2012-05, Vol.358, p.162-177
Hauptverfasser: Àlvarez Montaner, Josep, Boix, Alberto F., Zarzuela, Santiago
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Sprache:eng
Schlagworte:
Cartier algebras
Frobenius algebras
Frobenius, Àlgebra de
Matemàtiques i estadística
Stanley-Reisner rings
Àlgebra
Àrees temàtiques de la UPC
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container_title Journal of algebra
container_volume 358
creator Àlvarez Montaner, Josep
Boix, Alberto F.
Zarzuela, Santiago
description 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.
doi_str_mv 10.1016/j.jalgebra.2012.03.006
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source Elsevier ScienceDirect Journals Complete; Recercat; EZB-FREE-00999 freely available EZB journals
subjects Cartier algebras
Frobenius algebras
Frobenius, Àlgebra de
Matemàtiques i estadística
Stanley-Reisner rings
Àlgebra
Àrees temàtiques de la UPC
title Frobenius and Cartier algebras of Stanley–Reisner rings
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