Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

Oleg Gutik; Jimmie Lawson; Dušan Repovš

doi:10.1007/s00233-008-9112-2

Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

Group Theory 2009-03-19 v2 General Topology

Authors: Oleg Gutik , Jimmie Lawson , Dušan Repovš

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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 $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ 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.

Keywords

symmetric inverse semigroups finite rank semigroup closures tight ideal series algebraically closed continuous inversion compactifications

Cite

@article{arxiv.0804.1439,
  title  = {Semigroup Closures of Finite Rank Symmetric Inverse Semigroups},
  author = {Oleg Gutik and Jimmie Lawson and Dušan Repovš},
  journal= {arXiv preprint arXiv:0804.1439},
  year   = {2009}
}

Comments

With the participation of the new coauthor - Jimmie Lawson - the manuscript has been substantially revised and expanded. Accordingly, we have also changed the manuscript title

Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

Abstract

Keywords

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