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On irreducible modules over $ q$-skew polynomial rings and smash products


Author: Piotr Grzeszczuk
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
Published electronically: September 12, 2013
MathSciNet review: 3119181
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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\char93 H$, where $ H$ is a Hopf algebra generated by skew primitive elements.


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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

DOI: https://doi.org/10.1090/S0002-9939-2013-11794-6
Keywords: Irreducible module, skew polynomial ring, skew derivation
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
Article copyright: © Copyright 2013 American Mathematical Society