On nuclei of sup-$Sigma$-algebras

Abstract

‎In this paper‎, ‎algebraic investigations on sup-$Sigma$-algebras are presented‎. ‎A representation theorem for‎ ‎sup-$Sigma$-algebras in terms of nuclei and quotients is obtained‎. ‎Consequently‎, ‎the relationship between‎ ‎the congruence lattice of a sup-$Sigma$-algebra and the lattice of its nuclei is fully developed.