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In this paper, we study third power associative rings satisfying the identityWe prove that third power associative rings satisfying the identitywith characteristicsare power associative and associators generate nilpotent ideal with index of nilpotency. Furthermore, we prove that third power associative rings satisfying the identitywith commutators contained in the left nucleus and characteristicsare associative and commutative of degree five.

Third power associative rings satisfying a ( bc )= b ( ca )