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 λn 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. © 2008 Springer Science+Business Media, LLC.
Publication Source (Journal or Book title)
Gutik, O., Lawson, J., & Repovš, D. (2009). Semigroup closures of finite rank symmetric inverse semigroups. Semigroup Forum, 78 (2), 326-336. https://doi.org/10.1007/s00233-008-9112-2