How can i create a Rees-matrix semigroup? I've already read the definition of Rees-matrix semigroups, but I still can not imagine how to create one.
For example.:
I shall create a M(G;I;Lambda;P) semigroup where G is a group with 2 elements, the sets of indexes containe 2 elements as well and the P sandwitch matrix has NO zero element.
It will generate 2x2 matrices, but which matrices, and the most important: HOW CAN I GET THEM?
Thank You for reading this

is that ok to generate a group G={e,a} where ea=a=ae and aa=e, adjungate an zero element, so G0={0,e,a}??
Then the semigroup elements are 2x2 matrices, with only one non-zero element. So (a_ij)= a or e for all i and j in I and Lambda. So we get 8 matrixes and the 0 matrix.
The sandwitch matrix can be any of thoae 16 2x2 matrices which are includes only a and e elements.
IDK is that ok or not
