Closure operators and semilattice ordered algebras
Agata Pilitowska, Anna Zamojska-Dzienio · arXiv (Cornell University) · 2013
In a natural way one can lift any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A,F) its power algebra of subsets. Power algebras of non-empty subsets with additional operation of set-theoretical union are known as extended power algebras. We study connections between congruences on the extended power algebra defined on an algebra (A,F) and closure operators on a set A. Obtained correspondence allows to give an alternative description of the lattice of all subvarieties of semilattice ordered algebras.