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Huh, Chan; Kim, Hong Kee; Kim, Nam Kyun; Lee, Yang

Basic examples and extensions of symmetric rings. (English) Zbl 1078.16030

J. Pure Appl. Algebra 202, No. 1-3, 154-167 (2005).
A ring \(R\) with identity is called ‘symmetric’ if \(rst=0\) implies \(rts=0\) for all \(r,s,t\in R\). The authors discuss basic examples and extensions, and prove that a minimal noncommutative symmetric ring is of order 16 and is unique up to isomorphism. This ring is given in Example 2.5. They also construct more examples of symmetric rings and counterexamples to several naturally arising situations in the process.
Reviewer: Xue Weimin (Fujian)

Cited in 20 Documents

MSC:

16U80 Generalizations of commutativity (associative rings and algebras)
16U20 Ore rings, multiplicative sets, Ore localization
16P10 Finite rings and finite-dimensional associative algebras

Keywords:

reduced rings; minimal noncommutative symmetric rings; finite symmetric rings; classical right quotient rings; right Ore symmetric rings; extensions
PDFBibTeX XMLCite
\textit{C. Huh} et al., J. Pure Appl. Algebra 202, No. 1--3, 154--167 (2005; Zbl 1078.16030)
Full Text: DOI

References:

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