On Atomic Lattices

  • Lee, Seung-On (Dept. of Math., Chungbuk National University) ;
  • Yon, Yong-Ho (Dept. of Math., Chungbuk National University) ;
  • Hwang, In-Jae (Dept. of Com. Edu. Chungbuk National University)
  • Published : 2006.11.30

Abstract

The lattice originated from logic, not mathematics. Around 1880, Peirce thought that all the lattices were distributives, however $Schr{\"{o}}der$ corrected the error around 1890. In 1993, Birkhoff used the term lattice for the first time that had a different meaning from today's lattice. This paper introduces Peirce, and studies correlation among atomic lattices, atomistic lattices, J-lattices, strong lattices and distributive lattices.