Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2
On Zero Determinant Matrices that are Full
Authors:
Grigore CălugăreanuDepartment of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

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Horia F. PopDepartment of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

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Pages:
81–88
Online Publication Date:
08 Oct 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00008
Keywords:
full matrix; inner rank. zero determinant matrix; column-row decomposition; pre-Schreier ring
Open access

Column-row products have zero determinant over any commutative ring. In this paper we discuss the converse. For domains, we show that this yields a characterization of pre-Schreier rings, and for rings with zero divisors we show that reduced pre-Schreier rings have this property.

Finally, for the rings of integers modulo n, we determine the 2x2 matrices which are (or not) full and their numbers.

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    Cohn P. M. Bézout rings and their subrings. Proc. Camb. Philos. Soc. 64 (1968), 251-264.

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    Lockhart, J. M. and Warlow, W. P. Determinants of matrices over the integers modulo m. Mathematics Magazine 80, 3 (2007), 207-214.

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    McAdam, S. and Rush, D. E. Schreier rings. Bull. London Math. Soc. 10,1 (1978), 77-80.

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    Zafrullah, M. On a property of pre-Schreier domains. Comm. in Algebra 15, 9 (1987), 1895-1920.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
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ltoth@gamma.ttk.pte.hu

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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