Effective representations of path semigroups. (Q283339)

If \(S\) is a semigroup and \(\Bbbk\) a field, then the \textit{effective dimension} of \(S\) over \(\Bbbk\) is the minimal number \(n\in\{0,1,2,\ldots,\infty\}\) such that there is a representation of \(S\) by linear operators on a \(n\)-dimensional \(\Bbbk\)-vector space in which different elements of \(S\) are represented by different matrices. In the paper under review the author determines the effective dimension of path semigroups over uncountable fields and the effective dimension of truncated path semigroups over fields which are uncountable or of characteristic zero.