The lattice of algebraic closure operators

2014/11/20 by Kilpack, Martha Lee Hollist
#06A15 #06B23 #06B30 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1411.6497

Abstract

On an infinite set some closure operators are finitary (algebraic) while others are not. We can generalize this idea for a complete algebraic lattice letting the compact elements act as the finite sets. With this in mind, we will consider the set of algebraic closure operators on such a lattice. We will show this set forms a complete lattice that is also an algebraic lattice.

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