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Semigroup closures of finite rank symmetric inverse semigroups

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Abstract

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I n λ of the rank ≤ n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine

    Oleg Gutik

  2. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Jimmie Lawson

  3. Institute of Mathematics, Physics and Mechanics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana, 1000, Slovenia

    Dušan Repovš

Authors
  1. Oleg Gutik
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  2. Jimmie Lawson
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  3. Dušan Repovš
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Correspondence to Jimmie Lawson.

Additional information

Communicated by Karl H. Hofmann.

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Gutik, O., Lawson, J. & Repovš, D. Semigroup closures of finite rank symmetric inverse semigroups. Semigroup Forum 78, 326–336 (2009). https://doi.org/10.1007/s00233-008-9112-2

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