Abstract: Guenther Eigenthaler

CONGRUENCE CLASSES IN UNIVERSAL ALGEBRA

 

           Congruence relations play an important role when investigating universal algebras. On the one hand, the structure of the congruence lattice of a given algebra reveals much information on the underlying algebra. On the other hand, via congruence relations quotient algebras can be formed which may have "nicer" properties than the original algebras. Moreover, in many cases congruences are determined by some of their classes. For instance in the case of groups, rings and Boolean algebras, congruences are determined by each single one of their classes. The aim of the talk is to present some of the most important results concerning congruence classes, dependences between them as well as connections to subalgebras.