Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/25800
Author(s): Christian Lomp
Title: Ring theoretic aspects of weak Hopf actions
Issue Date: 2009
Abstract: Following Linchenko and Montgomery's arguments we show that the smash product of a semiprime module algebra, satisfying a polynomial identity and an involutive weak Hopf algebra is semiprime. We get new insight into the existence of non-trivial central invariant elements in non-trivial H-stable ideals of subdirect products of certain H-prime module algebras satisfying a polynomial identity by considering an adapted version of Kaplansky's theoremand by introducing a Brown-McCoy radical for module algebras. We extend Puczylowski and Smoktunowicz's description of the Brown-McCoy radical of a polynomial ring to module algebras and apply our result to left bialgebroidmeasurings, gradings and involutions. The paper finishes with an extension of results by Bergen et al. and Cohen at al. on irreducible module algebras to weak Hopf actions.
Description: Following Linchenko and Montgomery's arguments we show that the smash product of a semiprime module algebra, satisfying a polynomial identity and an involutive weak Hopf algebra is semiprime. We get new insight into the existence of non-trivial central invariant elements in non-trivial H-stable ideals of subdirect products of certain H-prime module algebras satisfying a polynomial identity by considering an adapted version of Kaplansk's theoremand by introducing a Brown-McCoy radical for module algebras. We extend Puczylowski and Smoktunowicz's description of the Brown-McCoy radical of a polynomial ring to module algebras and apply our result to left bialgebroidmeasurings, gradings and involutions. The paper finishes with an extension of results by Bergen et al. and Cohen at al. on irreducible module algebras to weak Hopf actions.
Subject: Álgebra, Matemática
Algebra, Mathematics
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
URI: https://repositorio-aberto.up.pt/handle/10216/25800
Document Type: Relatório Técnico
Rights: openAccess
License: https://creativecommons.org/licenses/by-nc/4.0/
Appears in Collections:FCUP - Relatório Técnico

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