The aim of the series of lectures is to present an introduction to
the theory of "factorizable" semigroups. Factorizable inverse monoids
arise in a natural way from certain group actions, and so they appear in
different areas of mathematics. In the theory of semigroups their study
goes back to the 1970's, and they became important mainly because they
turned out to constitute the counterpart of E-unitary inverse monoids in
McAlister's theory. The semigroup analogue of factorizable inverse
monoids called almost factorizable inverse semigroups were seeked for
and identified by Lawson in the 1990's just by this property. Later on,
these results were generalized for the class of straight locally inverse
semigroups by Dombi, and recently, for the class of weakly ample
semigroups by Gomes and the speaker, and for the class of orthodox
semigroups by Hartmann.
The topics of the lectures: 1.
Factorizable inverse monoids 2. Almost factorizable inverse
semigroups 3. Almost factorizability for straight locally inverse
semigroups, for weakly ample semigroups and for orthodox semigroups |