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

Abstract

<p>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 (<em>a, b, c</em>) - (<em>a, c, b</em>) = (<em>a</em>, [<em>b, c</em>], <em>d</em>) = 0, is associative. This generalizes a recent result by Y. Paul [7].</p>