Nilpotency classes of right nilpotent congruences
Bull. Korean Math. Soc. 1999 Vol. 36, No. 1, 139-146
Joohee Jeong
Kyungpook National University
Abstract : 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
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd