Amenable Partial Order On The Semilattice Of Regular Semigroups

This paper studies V-semilatticed amenable partially ordered regular semi-groups. The main results are in the following aspects:In this paper, V-semilatticed amenable partially ordered completely reg-ular semigroups are studied and introduced. It is proved that if (S,·,≤) is V-semilatticed amenable partially ordered completely regular semigroups, then (S,·) are clifford semigroups; At the same time, it is gotten several intersting corollaries. Also, it is proved that if (S,·,≤) is V-semilatticed amenable par-tially ordered completely simple semigroups, then S is latticed ordered groups; It showed that V-semilatticed amenable partially ordered completely simple semi-groups are group.In this paper, V-semilatticed amenable partially ordered locally E-unitary clifford semigroups are introduced and studied. It is testified that if (S,·,≤) is V-semilatticed amenable partially ordered locally E-unitary Clifford semigroups, then (S,·) is E-unitary clifford semigroups. Moreover, we establish one order-preserving monomorphism between subsemigroups Ae and Af of V-semilatticed amenable partially ordered E-unitary clifford semigroups, therefore, we ob-tain isomorphisms theory between subsemigroups Ae and Af of V-semilatticed amenable partially ordered E-unitary clifford semigroups.