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  • 1 Department of Mathematics and Computer Science, , Babeş-Bolyai University, Cluj-Napoca, , Romania
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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.

  • [1]

    Andrunakievich, V. A. and Ryabukhin, J. M. Rings without nilpotent elements, and completely prime ideals. Dokl. Akad. Nauk SSSR 180 (1968), 9-11. (in Russian)

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  • [2]

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

  • [3]

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

  • [4]

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

  • [5]

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

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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)

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

University of Pécs,
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Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Publication
Programme
2021 Volume 27 /N.S. 1/
Volumes
per Year
1
Issues
per Year
2
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)