关键词: 宽广(n, m) -半群, 拟恰当宽广（n, m）-半群, 恰当宽广（n, m）-半群, 格林-关系, (n, m) -半群

Abstract: We extend Green-relations from usual semigroups to (n,m)-semigroups. We further define broad (n,m)-semigroups, quasi adequate broad (n,m)-semigroups and adequate broad (n,m)-semigroups and address their fundamental properties.

Key words: (n,m)-semigroup, adequate broad (n,m)-semigroup, quasi adequate broad (n,m)-semigroup, Greenrelations, broad (n,m)-semigroup