journal6 ›› 2014, Vol. 35 ›› Issue (5): 13-17.DOI: 10.3969/j.issn.1007-2985.2014.05.004

• Mathematics • Previous Articles     Next Articles

Semisimplicity for Upper Continuous and Complete Modular Lattices

 NIU  Juan-Ning, LI  Qi-Sheng   

  1. (College of Mathematics and Statics,Jishou University,Jishou 416000,Hunan China)
  • Online:2014-09-25 Published:2014-10-30

Abstract: It is proved that for an upper continuous and complete  modular lattice L,L is locally atomic if and only if 1 is a join of atoms,and if and only if 1 is a join of independent atoms.Moreover,some conditions under which 1 can be expressed as a join of finite atoms are given.

Key words: complete lattice, semi-simplicity, independent set, compactly generated, upper continuous

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