Abstract:

     We generalize Green*relations from usual semigroups to (n,m)-semigroups and then define abundant (n,m) semigroups, adequate (n,m) semigroups and type A  (n,m)-semigroups. We also address their fundamental properties. Especially, we generalize a theorem about Munn semigroups.

Key words: (n,m)-semigroups, Green* relation, abundant , (n,m)-semigroups, adequate (n,m)-semigroups, (n,m)-semigroups of type A