Tight representations of \(0\)-\(E\)-unitary inverse semigroups.
Summary: We study the tight representation of a semilattice in \(\{0,1\}\) by some examples. Then we introduce the concept of the complex tight representation of an inverse semigroup \(S\) by the concept of the tight representation of the semilattice of idempotents \(E\) of \(S\) in \(\{0,1\}\). Specifically we describe the tight representation of a 0-\(E\)-unitary inverse semigroup and prove that if \(\sigma\) is a tight semilattice representation of the 0-\(E\)-unitary inverse semigroup \(S\) in \(\{0,1\}\), then \(\sigma\) is a complex tight representation.
scientific article; zbMATH DE number 5997787
scientific article