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On Topological Semigroups of Matrix Units

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Abstract

On the infinite semigroup of matrix units there exists no semigroup compact [countably compact] topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into a compact topological semigroup is annihilating. The semigroup of matrix units is algebraically h-closed in the class of topological inverse semigroups. Some H-closed minimal semigroup topologies on the infinite semigroup of matrix units are considered.

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Authors and Affiliations

  1. Pidsryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3b, Naukova Str., Lviv, 79060, and Department of Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine

    Oleg V. Gutik

  2. Department of Algebra, Pidsryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3b, Naukova Str., Lviv, 79060, Ukraine

    Kateryna P. Pavlyk

Authors
  1. Oleg V. Gutik
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  2. Kateryna P. Pavlyk
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Correspondence to Oleg V. Gutik or Kateryna P. Pavlyk.

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Gutik, O., Pavlyk, K. On Topological Semigroups of Matrix Units. Semigroup Forum 71, 389–400 (2005). https://doi.org/10.1007/s00233-005-0530-0

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  • DOI: https://doi.org/10.1007/s00233-005-0530-0

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