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Symmetric Utumi quotient rings of Ore extensions by skew derivations


Authors: Chen-Lian Chuang and Yuan-Tsung Tsai
Journal: Proc. Amer. Math. Soc. 138 (2010), 3125-3133
MSC (2010): Primary 16S36, 16S85, 16W25
DOI: https://doi.org/10.1090/S0002-9939-10-10342-6
Published electronically: April 6, 2010
MathSciNet review: 2653937
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Abstract: Let $ R$ be a ring, $ X$ a sequence of noncommuting indeterminates $ x_1,x_2,\ldots$ and $ D$ a sequence of skew derivations $ \delta_1,\delta_2,\ldots$, where each $ \delta_i$ is a $ \sigma_i$-derivation of $ R$. The Ore extension of $ R$ by $ D$, denoted by $ R[X;D]$, is the ring generated by $ R$ and $ X$ subjected to the rule $ x_ir=\sigma_i(r)x_i+\delta_i(r)$ for each $ i$. If $ \vert X\vert\ge 2$ and $ R$ is a domain, we show that the symmetric maximal ring of quotients of $ R[X;D]$ is equal to $ U_s(R)[X;D]$, where $ U_s(R)$ is the symmetric maximal ring of quotients of $ R$.


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Additional Information

Chen-Lian Chuang
Affiliation: Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
Email: chuang@math.ntu.edu.tw

Yuan-Tsung Tsai
Affiliation: Department of Applied Mathematics, Tatung University, Taipei 104, Taiwan
Email: yttsai@ttu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-10-10342-6
Keywords: Domain, skew derivations, Ore extension, skew polynomial ring, symmetric Utumi quotient ring, symmetric maximal ring of quotients
Received by editor(s): September 17, 2009
Received by editor(s) in revised form: December 16, 2009
Published electronically: April 6, 2010
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.