Bulletin of the
Korean Mathematical Society BKMS

It is known that a right nilpotent congruence $\beta $ on a finite algebra \bA\ is also left nilpotent \cite{kearns93}. The question on whether the left nilpotency class of $\beta$ is less than or equal to the right nilpotency class of $\beta$ is still open. In this paper we find an upper limit for the left nilpotency class of $\beta$. In addition, under the assumption that $\mathbf{1}\not\in\typ\{\bA\}$, we show that $(\beta]^k = [\beta)^k$ for all $k\ge 1$. Thus the left and right nilpotency classes of $\beta$ are the same in this case.

Keywords: commutator, nilpotent congruence, nilpotency class

MSC numbers: 08A05