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Linear and Multilinear Algebra Volume 64, 2016 - Issue 5
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Articles

Homomorphisms of commutativity relation

Gregor DolinarFaculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia.Correspondence[email protected]
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Bojan KuzmaDepartment of Mathematics, University of Primorska, Koper, Slovenia.;IMFM, Ljubljana, Slovenia.View further author information
Pages 897-922 | Received 27 Feb 2015, Accepted 22 Jun 2015, Published online: 24 Jul 2015
 
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Abstract

Surjective maps which preserve commutativity relation on matrices over algebraically closed fields are classified. Unlike previous results on commutativity preservers, it is assumed that maps preserve commutativity only in one direction and have no additional structure like additivity. Our techniques combine graph theory, linear algebra and projective geometry.

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Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was partially supported by Ministry of Education, Science and Sport of Slovenia.

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