Semigroups with midunits
Janet E. Ault · Transactions of the American Mathematical Society · 1974
A semigroup has a midunit u if a u b = a b aub = ab for all a and b . It is the purpose of this paper to explore semigroups with midunits, and to find an analog to the group of units. In addition, two constructions will be given which produce some semigroups with midunits, and an abstract characterization will be made of certain of these semigroups.