Brandt半群的正规子半群格  

Normal subsemigroup lattices of Brandt semigroups

作　　者：田振际[1] 王宾 TIAN Zhen-ji;WANG Bin(School of Science,Lanzhou Univ.of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2018年第5期155-158,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11261030)

摘　　要：研究并刻画了任意逆半群S的正规子半群格Subn S和S的最大群同态象S/σ的正规子群格Subn(S/σ)之间的基本关系.证明了Brandt半群S的正规子半群格Subn S是分配格,当且仅当S或者是带零的局部循环群,或者是Brandt半群B5.同时也给出了Brandt半群S的正规子半群格Subn S是0-分配格的充分必要条件.The basic relationship of normal subsemigroup lattices of arbitrary counter-semigroups(S),(Subn S)to normal subgroup lattices of maximal group homomorphic image(S/σ)of S(Subng(S/σ))is studied and depicted in this article.It is also proved that normal subsemigroup lattice of S of Brandt semigroup(B)would be distributive lattice if and only if S was either a locally cyclic group with zero or Brandt semigroup(B 5).Meantime,the necessary and sufficient conditions are given for that the normal subsemigroup lattice is a 0-distributive lattice of S of Brandt semigroup.

关 键 词：正规子半群格 分配格 0-分配格 BRANDT半群 

分 类 号：O152[理学—数学]