Third power associative, antiflexible rings satisfying (<italic>a</italic>,<italic>b</italic>,<italic>ac</italic>) = <italic>a</italic>(<italic>a</italic>,<italic>b</italic>,<italic>c</italic>).

In this paper, we study third power associative, antiflexible rings satisfying the identity (<italic>a</italic>,<italic>b</italic>,<italic>ac</italic>) = <italic>a</italic>(<italic>a</italic>,<italic>b</italic>,<italic>c</italic>). We prove that third power associative, antiflexible rings satisfying the identity (<italic>a</italic>,<italic>b</italic>,<italic>ac</italic>) = <italic>a</italic>(<italic>a</italic>,<italic>b</italic>,<italic>c</italic>) with characteristic ≠2,3 are associative of degree 5. As a consequence of this result, we prove that a third power associative semiprime antiflexible ring satisfying the identity (<italic>a</italic>,<italic>b</italic>,<italic>ac</italic>) = <italic>a</italic>(<italic>a</italic>,<italic>b</italic>,<italic>c</italic>) is associative. [ABSTRACT FROM AUTHOR]