Some open problems in the structure theory of regular semigroups (Q1597721)

The author recalls the relevant structure theorems for inverse semigroups involving, respectively, fundamental inverse semigroups, \(E\)-unitary inverse semigroups and factorizable inverse semigroups, and she formulates research problems which ask for a generalization of the reviewed structure theorems to wider classes of regular semigroups such as locally inverse semigroups or orthodox semigroups. Several variants of the notion of a semidirect product of a regular semigroup by a group are brought to the attention of the reader. Also included are problems concerning free inverse semigroups on commuting generators and problems on commutative nilsemigroups.