Brandt半群的正规子半群格
|
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 Sof Brandt semigroup(B)would be distributive lattice if and only if S was either a locally cyclic group with zero or Brandt semigroup(B5).Meantime,the necessary and sufficient conditions are given for that the normal subsemigroup lattice is a 0-distributive lattice of Sof Brandt semigroup.
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 Sof Brandt semigroup(B)would be distributive lattice if and only if S was either a locally cyclic group with zero or Brandt semigroup(B5).Meantime,the necessary and sufficient conditions are given for that the normal subsemigroup lattice is a 0-distributive lattice of Sof Brandt semigroup.
引文
[1]TAMURA T.Semigroups and their subsemigroup lattices[J].Pacific J Math,1963,13:725-735.
[2]JONES P R.Semimodular inverse semigroups[J].J London Math Soc,1978,17(2):446-456.
[3]JONES P R.Distributive inverse semigroups[J].J London Math Soc,1978,17(2):457-466.
[4]JONES P R.Lattice isomorphisms of inverse semigroups[J].Glasgow Math J,2004,46:193-204.
[5]JOHNSTON K G,JONES P R.Semidistributive inverse semigroups[J].J Australian Math Soc,2001,71:37-51.
[6]JOHNSTON K G,JONES P R.Modular inverse semigroups[J].J Australian Math Soc,1987,43:47-63.
[7]TIAN Z J.The lattice of full subsemigroups of an inverse semigroup[J].Semigroup Forum,2006,73:457-469.
[8]田振际.π逆半群的子半群格[M].北京:科学出版社,2007.
[9]田振际.π逆半群格是模格的π逆半群[J].系统科学与数学,1997,17(3):226-231.
[10]HOWIE J M.Fundamentals of semigroup theory[M].Oxford:Clarendon Press,1995.
[11]PETRICH M.Inverse semigroups[M].New Yoke:Wiley,1984.
[12]SHEVRIN V M.Semigroups with∧-semidistributive subsemigroup lattice[J].Semigroup Forum,1985,31:47-68.
[13]SHEVRIN L N,OVSYANNIKOV A J.Semigroups and their subsemigroups lattices[J].Semigroup Forum,1983,27:1-154.
[2]JONES P R.Semimodular inverse semigroups[J].J London Math Soc,1978,17(2):446-456.
[3]JONES P R.Distributive inverse semigroups[J].J London Math Soc,1978,17(2):457-466.
[4]JONES P R.Lattice isomorphisms of inverse semigroups[J].Glasgow Math J,2004,46:193-204.
[5]JOHNSTON K G,JONES P R.Semidistributive inverse semigroups[J].J Australian Math Soc,2001,71:37-51.
[6]JOHNSTON K G,JONES P R.Modular inverse semigroups[J].J Australian Math Soc,1987,43:47-63.
[7]TIAN Z J.The lattice of full subsemigroups of an inverse semigroup[J].Semigroup Forum,2006,73:457-469.
[8]田振际.π逆半群的子半群格[M].北京:科学出版社,2007.
[9]田振际.π逆半群格是模格的π逆半群[J].系统科学与数学,1997,17(3):226-231.
[10]HOWIE J M.Fundamentals of semigroup theory[M].Oxford:Clarendon Press,1995.
[11]PETRICH M.Inverse semigroups[M].New Yoke:Wiley,1984.
[12]SHEVRIN V M.Semigroups with∧-semidistributive subsemigroup lattice[J].Semigroup Forum,1985,31:47-68.
[13]SHEVRIN L N,OVSYANNIKOV A J.Semigroups and their subsemigroups lattices[J].Semigroup Forum,1983,27:1-154.