Green’s relations for 2 × 2 matrices over linearly ordered abelian groups - Marilyn Kutti; Valdis Laan (Proceedings of the Estonian Academy of Sciences)
We consider semigroups of 2 Ã 2 matrices over linearly ordered abelian groups with respect to multiplication, which is defined similarly to tropical algebra. We study Greenâs relations on such semigroups. In particular, we describe the R-, L- and H-classes of such semigroups and give a simple criterion for determining whether two matrices are D-related. We prove that the D-relation coincides with the J-relation. We also study maximal subgroups of such semigroups. It turns out that if the abelian group is divisible, then these maximal subgroups can have two different forms.