Breaking the Weak Commutative Property of Finite Boolean Subalgebra Triples
MetadataShow full item record
Heindorf and Shapiro studied commuting pairs of Boolean subalgebras and showed that Boolean subalgebra pairs that commute retain their commutativity property after taking the exponential functor. Recently Milovich introduced the concept of commuting n-tuples and weakly commuting n-tuples of Boolean subalgebras. In particular, Milovich non-constructively proved that there exists a case where by applying the exponential functor to a triple, of finite Boolean subalgebras, the weakly commuting property is destroyed. The purpose of this paper is to find explicit examples of triples of finite subalgebras that weakly commute but when the exponential functor is applied, the weak commutativity property of this triple is destroyed. Using Python, a high level programming language, it was determined that the four atom finite Boolean Algebra has a triple of subalgebras whose weakly commuting property is destroyed when the exponential functor is applied. Furthermore, we show that the three atom finite Boolean Algebra has no triple of subalgebras whose weakly commuting property is destroyed when the exponential functor is applied.