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 |