Semigroup closures of finite rank symmetric inverse semigroups

被引：0
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作者：
Oleg Gutik
Jimmie Lawson
Dušan Repovš
机构：
[1] Ivan Franko Lviv National University,Department of Mechanics and Mathematics
[2] Louisiana State University,Department of Mathematics
[3] University of Ljubljana,Institute of Mathematics, Physics and Mechanics, Faculty of Mathematics and Physics
来源：
Semigroup Forum | 2009年 / 78卷
关键词：
Topological semigroup; Semitopological semigroup; Topological inverse semigroup; Symmetric inverse semigroup of finite transformations; Algebraically closed semigroup; -unstable set; Semigroup with a tight ideal series;
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摘要：
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 Iλn 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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