Congruences on Zappa-Sz\'{e}p Products of Semilattices with An Identity and Groups
Received:April 09, 2011  Revised:October 31, 2011
Key Words: Zappa-Sz\'{e}p product   congruence   congruence pairs.  
Fund Project:
Author NameAffiliation
Jiangping XIAO School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
Yonghua LI School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
Hits: 2861
Download times: 2438
Abstract:
      Let $P=E\bowtie G$ be a Zappa-Sz\'{e}p product of a semilattice $E$ with an identity and a group $G$. In this paper, we first introduce the concept of congruence pairs for $P$, and then prove that every congruence on $P$ can be described by such a congruence pair. In fact the congruence lattice on $P$ is lattice-isomorphic to the set of all congruence pairs for $P$. Finally, we characterize group congruences on $P$.
Citation:
DOI:10.3770/j.issn:2095-2651.2012.06.007
View Full Text  View/Add Comment