Graphical algebras -- a new approach to congruence lattices
A graphical algebra is a complete lattice together with some special mapping which generalizes the graphical composition introduced by \textit{H.Werner} [Colloq. Math. Soc. Janos Bolyai 14, 433--453 (1976; Zbl 0363.06002)]. Both the abstract characterization as well as one based on some special class of graphs are given and studied in full detail. The main result is the finding of sufficient conditions for a graphical algebra to be a congruence graphical algebra. As a corollary the author obtains the well-known result that any algebraic lattice is the congruence lattice of an algebra [\textit{G. Grätzer} and \textit{E. T. Schmidt}, Acta Sci. Math. 24, 34--50 (1963; Zbl 0117.26101)]. An extensive list of open problems concludes the paper.
scientific article; zbMATH DE number 5886738