A note on rings with involution (Q1087619)

Let R be a ring with involution * and \(\rho\) a right ideal of R. The paper shows that if every symmetric element s satisfies \(s^ n=0\), where n is fixed, then \(\rho^*\rho \subset {\mathcal L}(R)\), the lower nil radical of R. This turns into a well-known result of Levitzki in case the involution is trivial.