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Advances in Mathematical Physics
Volume 2011 (2011), Article ID 546058, 9 pages
http://dx.doi.org/10.1155/2011/546058
Research Article

Quantum Groupoids Acting on Semiprime Algebras

1Instituto Superior De Contabilidade e Administração de Coimbra, Quinta Agrícola-Bencanta, 3040-316 Coimbra, Portugal
2Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua Campo Alegre 687, 4169-007 Porto, Portugal

Received 30 March 2011; Accepted 5 June 2011

Academic Editor: Olaf Lechtenfeld

Copyright © 2011 Inês Borges and Christian Lomp. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Following Linchenko and Montgomery's arguments we show that the smash product of an involutive weak Hopf algebra and a semiprime module algebra, satisfying a polynomial identity, is semiprime.