Ring theoretic aspects of weak Hopf actions

• Type: Technical Report
• Date: 2009

Authors

Christian Lomp (Author) FCUP

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics > Algebra

Associated Institutions

MPI - Max Plank Institut

Other information

Resumo (PT): 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 theorem and 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 bialgebroid measurings, 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.

Abstract (EN): 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 theorem and 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 bialgebroid measurings, 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.

Language: English

Type (Professor's evaluation): Scientific

Reference: MPIM2009-30

No. of pages: 16