摘要
本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过素根定理证明了序半群S是阿基米德序子半群的链当且仅当S是阿基米德序子半群的半格且S的所有素理想关于集合的包含关系构成链.
In this paper,some characterizations for an ordered semigroup S to be a chain of archimedean（r-archimedean,t-archimedean） ordered subsemigroups are given by some binary relations on S and the radical subsets of ideals（right ideals,bi-ideals） of S.Furthermore,we prove that semiprimary ordered semigroups are exactly chains of archimedean ordered semigroups. Finally,using the prime radical theorem,we prove that an ordered semigroup S is a chain of archimedean ordered subsemigroups if and only if S is a semilattice of archimedean ordered subsemigroups and all prime ideals of S form a chain.
出处
《数学进展》
CSCD
北大核心
2011年第1期119-125,共7页
Advances in Mathematics（China）
基金
supported by NSFC(No.10961014)
the Guangdong Provincial Natural Science Foundation of China(No.0501332)
the Anhui Provincial Excellent Youth Talent Foundation(No.2009SQRZ149)
the Fuyang Normal College Youth Foundation(No.2008LQ11)
关键词
序半群
素理想
准素理想
阿基米德(右阿基米德
t-阿基米德)序半群
半格
ordered semigroup
prime ideal
semiprimary ideal
archimedean（r-archimedean
t-archimedean） ordered semigroup
semilattice
