Symmetric Utumi quotient rings of Ore extensions by skew derivations
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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 $|X|\ge 2$ 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 $R$.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2653937