Ortho-u-monoids

In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E(S)-semiabundant semigroups. After introducing the concept of (∼)-Green’s relations, and obtaining some important properties of (∼)-Green’s relations and super E(S)-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the (∼)-Green’s relations, and the semi-spined product of semigroups.