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

DOI:
https://doi.org/10.1090/S0002-9939-2011-11153-5

Published electronically:
August 18, 2011

MathSciNet review:
2869132

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a field, and let be an automorphism of of finite order. Let be the quotient ring of the skew polynomial ring . Then any order in which contains and its center is a valuation ring of the center of is a crossed-product algebra , where is some normalized 2-cocycle. Associated to is a subgroup of and a graph. In this paper, we determine the connections between hereditary-ness and maximal order properties of and the properties of , and the graph of .

**1.**P. M. Cohn,*Algebra*, Vol. II, John Wiley & Sons, New York, 1977. MR**0530404 (58:26625)****2.**J. Gráter,*Prime PI-rings in which finitely generated right ideals are principal*, Forum Math.**4**(1992), 447-463. MR**1176882 (93i:16026)****3.**D. E. Haile,*Crossed-product orders over discrete valuation rings*, J. Algebra**105**(1987), 116-148. MR**871749 (88b:16013)****4.**J. S. Kauta,*Integral semihereditary orders, extremality, and Henselization*, J. Algebra**189**(1997), 226-252. MR**1438175 (98d:16030)****5.**I. Reiner,*Maximal Orders*, Academic Press, London, 1975. MR**0393100 (52:13910)****6.**A. R. Wadsworth,*Dubrovin valuation rings and Henselization*, Math. Ann.**283**(1989), 301-328. MR**980600 (90f:16009)**

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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:
https://doi.org/10.1090/S0002-9939-2011-11153-5

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