Factorizable inverse monoids.
An inverse monoid \(S\) is called `factorizable' provided that it decomposes into a product \(UE\) of its group \(U\) of units and its semi-lattice \(E\) of idempotents. The paper under review is a survey of the algebraic theory of factorizable inverse monoids. The paper starts with a short historical overview. This goes over to the structure theory of factorizable inverse monoids, where the author describes properties of Green's relations, subgroups and idempotents. The next part contains a discussion on submonoids, congruences and presentations. In the last part of the paper the author presents many examples, including (the factorizable part of) the symmetric inverse monoid, the dual symmetric inverse monoid, the coset monoid, the Galois inverse monoid, reflection monoids and Renner monoids.
scientific article; zbMATH DE number 5730949
scientific article