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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

Online
ISSN
1572-9176
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Idempotent matrices with invertible transpose

Grigore Călugăreanu
Published Online: 2019-06-13 | DOI: https://doi.org/10.1515/gmj-2019-2034

Abstract

We prove that if the transpose of every 2×2 idempotent matrix over a division ring D, different from the identity matrix, is not invertible, then D is commutative.

Keywords: Idempotent matrix; invertible transpose; commutators; division ring

MSC 2010: 15B99; 16K99; 15A03; 15A09

References

  • [1]

    R. N. Gupta, Nilpotent matrices with invertible transpose, Proc. Amer. Math. Soc. 24 (1970), 572–575. CrossrefGoogle Scholar

  • [2]

    N. Jacobson, Lectures in Abstract Algebra. Vol. II. Linear Algebra, D. Van Nostrand, Toronto, 1953. Google Scholar

About the article

Received: 2017-11-14

Revised: 2018-09-21

Accepted: 2018-09-26

Published Online: 2019-06-13


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2034.

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