Authors:
Karin Cvetko-Vah Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

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Damjana Kokol Bukovšek Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

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Tomaž Košir Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

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Ganna Kudryavtseva Centre for systems and information technologies, University of Nova Gorica, Vipavska cesta 13, p.p. 301, SI-5001 Nova Gorica, Slovenia

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Abstract

We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part of the symmetric inverse semigroup is 2np+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality.

  • [1] Bernik, J., Drnovšek, R., Kokol Bukovšek, D., Košir, T., Omladič, M. 2008 Reducibility and triangularizability of semitransitive spaces of operators Houston J. Math. 34 235247.

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  • [2] Bernik, J., Drnovšek, R., Kokol Bukovšek, D., Košir, T., Omladič, M. and Radjavi, H., On semitransitive Jordan algebras of matrices, to appear in J. Alg. Appl.

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  • [3] Bernik, J., Grunenfelder, L., Mastnak, M., Radjavi, H., Troitsky, V. G. 2005 On semitransitive collections of operators Semigroup Forum 70 436450 .

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  • [4] Cvetko-Vah, K., Kokol Bukovšek, D., Košir, T., Kudryavtseva, G., Lavrenyuk, Ya., Oliynyk, A. 2009 Semitransitive subsemigroups of the symmetric inverse semigroups Semigroup Forum 78 138147 .

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  • [5] East, J. 2006 A presentation of the singular part of the symmetric inverse monoid Comm. Algebra 34 16711689 .

  • [6] Ganyushkin, O., Mazorchuk, V. 2009 Classical Finite Transformation Semigroups, an Introduction Algebra and Applications 9 . Springer Verlag.

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  • [7] Maltcev, V., Mazorchuk, V. 2007 Presentation of the singular part of the Brauer monoid Math. Bohem. 132 297323.

  • [8] Radjavi, H., Troitsky, V. G. 2009 Semitransitive subspaces of operators Linear and Multilinear Algebra 57 111 .

  • [9] Rosenthal, H., Troitsky, V. G. 2005 Strictly semi-transitive operator algebras J. Operator Theory 53 315329.

  • [10] Semitransitivity Working Group at LAW’05, Bled 2006 Semitransitive subspaces of matrices Electronic Journal of Linear Algebra 15 225238.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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