On power-associativity of algebras with no nonzero joint divisor of zero and containing a nonzero central idempotent.

We prove that, if A is an algebra (over a field of characteristic zero) with no nonzero joint divisor of zero and containing a nonzero central idempotent, and if A satisfies the identities (x p , x q , x r) = 0 and (x p ′ , x q ′ , x r ′) = 0 with exponents p , q , r , p ′ , q ′ , r ′ belonging to {1, 2} such that p ≠ r , (p ′ , q ′ , r ′) ≠ (p , q , r) and (p ′ , q ′ , r ′) ≠ (3 − r , 3 − q , 3 − p) , then A is a unital power-associative algebra. [ABSTRACT FROM AUTHOR]