Minimal Freeness and Commutativity
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Apseudobasis for an abstract algebraA is a subsetX ofA such that every mappingX intoA extends uniquely to an endomorphism onA. A isminimally free ifA has a pseudobasis. In this paper we look at how minimal freeness interacts with various notions of commutativity (e.g., “operational” commutativity in the algebra, usual commutativity in the endomorphism monoid of the algebra). One application is a complete classification of minimally free torsion abelian groups.