Third power associative, antiflexible rings satisfying (a, b, bc) = b(a, b, c)

Abstract

In this article, we study third power associative, antiflexible rings satisfying the identity $(a,b,bc)=b(a,b,c).$ We prove that third power associative, antiflexible rings satisfying the identity $(a,b,bc)=b(a,b,c)$ with characteristic $\ne 2,3$ are associative of degree five. As a consequence of this result, we prove that a third power associative semiprime antiflexible ring satisfying the identity $(a,b,bc)=b(a,b,c)$ is associative.

Keywords:

• Antiflexible ring
• associative of degree five
• semiprime ring
• third power associative

2010 Mathematics Subject Classification:

• 17D99
• 17A05

Disclosure statement

No potential conflict of interest was reported by the authors.