On a class of Dubreil-Jacotin semigroups (Q1780016)

If \(S\) is a strong Dubreil-Jacotin semigroup and \(G\) is the set of residuals of the bimaximum element \(\xi\) then \(S\) is said to split if \(G\) is a subgroup of \(S\). It is shown that this occurs if and only if \(\xi\) is idempotent and \(G\) coincides with the group \(\mathcal H\)-class \(H_\xi\). If \(\xi\) is an identity element then \(S\) is said to be integral. Here the structure of split integral Dubreil-Jacotin semigroups is described.