摘要
引入广义格半群的概念 ,进而对广义格半群与格半群以及相应的理想和 sl理想的相互关系及区别进行了讨论 ,指出格半群是广义格半群 ,反之则不一定 ,在广义格半群中理想集 I( S)是完备格 ,而 sl理想集却不能构成格 ,在格半群中 ,sl理想集是格 ,但是两个 sl理想的上确界不等于其并 ,广义格半群中的理想均能生成 sl理想 .
This paper comes up with the concept of the general lattice semigroup and discusses the correlation and differentiation of the general lattice semigroup,the lattice semigroup and ideal and sl ideal,pointing out that any lattice semigroup is a general lattice semigroup,and vice versa.In the general lattice semigroup it is complete lattice that the ideal set I(S),but the sl ideal set SL(S) isn't the lattice.In the lattice semigroup the sl ideal set SL(S) is lattice,but the supremum of two sl ideals is not the same as its union,the ideal in the general lattice semigroup can generate all sl ideals.
出处
《广西师范学院学报（自然科学版）》
2002年第3期7-10,共4页
Journal of Guangxi Teachers Education University(Natural Science Edition)
基金
陕西理工学院科研基金资助项目 ( 2 0 0 0 xy0 0 0 7)
关键词
广义格半群
格半群
理想
sl理想
完备格
序半群
偏序集
理想集
general lattice semigroup
lattice semigroup
ideal
sl ideal
ideal set I(S)
sl ideal set SL(S).
