一类序半群的理想格

The Lattice of Ideals of Some Ordered Semigroups

证明了一个格 L同构于一个满足条件任何两个主理想的交仍为主理想的序半群的理想格的充分必要条件是格 L满足条件 (* ) :1) L是分配的完备格 ;2 ) L的任意两个非零元素的交仍是非零元 ;3) L的每个元为 L的完备并不可约的元素并 ;4 ) L的所有完备的并不可约元素集 P是∧-半格 .

The aim of this paper is to prove that a lattice L is isomorphic to the lattice of ideals of the ordered semigroup S satisfying that the intersection of any two principal ideals of S is also a principal ideal of S if and only if L satisfies the condition():1) L is a distributive and complete lattice;2) The intersection of any two non zero elements of L is also a non zero element of L ;3) Every element of L is the union of compact and join irreducible elements of L ;4) The subset P of all compact and join irreducible elements of L is a ∧ semilattice.