Rings with (a, b, c) = (a, c, b) and (a, [b, c]d) = 0: a case study using albert

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 asociative. This generalizes a recent result by Y. Paul [7].

Keywords:

• Identity
• nonassociative polynomial
• nonassociative ring
• algebra

AMS (MOS) Subject Classification:

• 17D99
• 68N99

C.R. Categories:

• 1.1.3 (Special-purpose algebraic systems)
• 1.1.4 (Applications)

^*This research was partially supported by NSF Grant #CCR8905534.

^*This research was partially supported by NSF Grant #CCR8905534.

Notes

^*This research was partially supported by NSF Grant #CCR8905534.