Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

Details Semigroup Closures of Finite Rank Symmetric Inverse Semigroups Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

2008-04-09

arxiv.org/abs/0804.1439v2

Semigroup Forum 78:2 (2009), 326-336.

Mathematics

Group Theory

With the participation of the new coauthor - Jimmie Lawson - the manuscript has been substantially revised and expanded. Accor

Scientific paper

10.1007/s00233-008-9112-2

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.

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