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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hereditary orders in the quotient ring of a skew polynomial ring


Author: John S. Kauta
Journal: Proc. Amer. Math. Soc. 140 (2012), 1473-1481
MSC (2010): Primary 16S35, 16S36, 16E60; Secondary 13F30
Published electronically: August 18, 2011
MathSciNet review: 2869132
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Abstract: Let $ K$ be a field, and let $ \sigma$ be an automorphism of $ K$ of finite order. Let $ K(X;\sigma)$ be the quotient ring of the skew polynomial ring $ K[X;\sigma]$. Then any order in $ K(X;\sigma)$ which contains $ K$ and its center is a valuation ring of the center of $ K(X;\sigma)$ is a crossed-product algebra $ A_f$, where $ f$ is some normalized 2-cocycle. Associated to $ f$ is a subgroup $ H$ of $ \langle\sigma\rangle$ and a graph. In this paper, we determine the connections between hereditary-ness and maximal order properties of $ A_f$ and the properties of $ H$, $ f$ and the graph of $ f$.


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Additional Information

John S. Kauta
Affiliation: Department of Mathematics, Faculty of Science, Universiti Brunei Darussalam, Bandar Seri Begawan, BE1410, Brunei
Email: john.kauta@ubd.edu.bn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11153-5
PII: S 0002-9939(2011)11153-5
Received by editor(s): September 21, 2009
Received by editor(s) in revised form: January 8, 2011
Published electronically: August 18, 2011
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2011 American Mathematical Society