On irreducible modules over $q$-skew polynomial rings and smash products
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Abstract:
Let $M$ be an irreducible left module over a $q$-skew polynomial ring $R[x;\sigma ,\delta ]$. We give sufficient conditions for the complete reducibility of $M$ considered as a module over the coefficient ring $R$. We apply it to irreducible modules over smash product $R\#H$, where $H$ is a Hopf algebra generated by skew primitive elements.References
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Additional Information
- Piotr Grzeszczuk
- Affiliation: Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland
- Email: piotrgr@pb.edu.pl
- Received by editor(s): November 19, 2011
- Received by editor(s) in revised form: February 26, 2012
- Published electronically: September 12, 2013
- Additional Notes: The author was supported in part by the grant MNiSW nr N N201 268435 and by the grant S/WI/1/2011 of Białystok University of Technology.
- Communicated by: Birge Huisgen-Zimmermann
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 59-69
- MSC (2010): Primary 16N20, 16S36, 16W25, 16S40
- DOI: https://doi.org/10.1090/S0002-9939-2013-11794-6
- MathSciNet review: 3119181