Rings with (a, b, c) = (a, c, b) and (a, [b, c]d) = 0: A Case Study Using Albert

Date
1993
Authors
Hentzel, Irvin
Hentzel, Irvin
Jacobs, D. P.
Kleinfeld, Erwin
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Altmetrics
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Research Projects
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Mathematics
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Abstract

Albert is an interactive computer system for building nonassociative algebras [2]. In this paper, we suggest certain techniques for using Albert that allow one to posit and test hypotheses effectively. This process provides a fast way to achieve new results, and interacts nicely with traditional methods. We demonstrate the methodology by proving that any semiprime ring, having characteristic ≠ 2, 3, and satisfying the identities (a, b, c) - (a, c, b) = (a, [b, c], d) = 0, is associative. This generalizes a recent result by Y. Paul [7].

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<p>This is an Accepted Manuscript of an article published by Taylor & Francis as Hentzel, Irvin Roy, D. P. Jacobs, and Erwin Kleinfeld. "Rings with (a, b, c)=(a, c, b) and (a,[b, c] d)= 0: a case study using albert." <em>International journal of computer mathematics</em> 49, no. 1-2 (1993): 19-27. doi: <a href="http://dx.doi.org/10.1080/00207169308804211%20" target="_blank">10.1080/00207169308804211</a>. Posted with permission. </p>
Keywords
identity, nonassociative polynomial, nonassociativering, algebra
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