Research On Several Kinds Of Partial Order Semigroups

Algebraic theory of partially ordered semigroups is one of the most im-portant fields of algebra. This paper mainly studies several classes of partially ordered semigroups. It mainly achieves in the following aspects:(1) The V-semilatticed partially ordered regular semigroup is studied. It shows that if the partial order≤of V-semilatticed partially ordered regular semigroups is the extension of the natural partial order≤, then (S,·) is an inverse semigroup. Moreover, if<is an amenable partial order on S, then (S,·) is a Clifford semigroup.(2) The V-semilatticed partially ordered abundant semigroup is studied. We prove that if the partial order≤of V-semilatticed partially ordered abundant semigroups is the extension of the natural partial order≤, then (S,·) is an adequate semigroup.(3) The Semilattice-ordered adequate semigroup is studied. It is proved that every semilattice-ordered adequate semigroup can be embeded in the semilattice-ordered endorphism semigroup of its additive reduct.