Minimal Freeness and Commutativity
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A pseudobasis for an abstract algebra A is a subset X of A such that every mapping X into A extends uniquely to an endomorphism on A. A is minimally free if A 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.
Bankston, Paul, "Minimal Freeness and Commutativity" (1992). Mathematics, Statistics and Computer Science Faculty Research and Publications. 169.
Algebra Universalis, Vol. 29, No. 1 (March 1992): 88-108. DOI.