纯阿基米德半群与其理想之间的等价关系

Discussion of Pure Archimedean Semigroup

在阿基米德半群的性质的基础上讨论得出了关于纯阿基米德半群与其理想之间的等价关系.得到结论:半群S的每一个理想是纯阿基米德半群I(S)(S中全体理想之并)是纯阿基米德半群S满足以下条件之一:S是纯阿基米德半群或S有极大理想M,M是纯阿基米德半群且M M a,a∈S\M.

Equivalent relation between a pure Archimedean semigroup and its ideals is discussed for an equivalent semigroups, every proper ideal of S is pure archimedean semigroup. I（S）, the union of all the proper ideals of a semigroup S is pure Archimedean semigroup and S satisfies one of the following conditions where S is a pure archimedean semigroup or S has maximal left ideal M which is an pure archimedean semigroup with M C M a, a∈ S／M.