Title

Minimal Freeness and Commutativity

Document Type

Article

Language

eng

Format of Original

21 p.

Publication Date

3-1992

Publisher

Springer

Source Publication

Algebra Universalis

Source ISSN

0002-5240

Original Item ID

doi: 10.1007/BF01190758

Abstract

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.

Comments

Algebra Universalis, Vol. 29, No. 1 (March 1992): 88-108. DOI.