The pasting constructions of lattice ordered effect algebras

Authors:
Yongjian Xie;Yongming Li;Aili Yang
Affiliations:
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China;College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China and College of Computer Science, Shaanxi Normal University, Xi'an 710062, China;College of Science, Xi'an University of Science and Technology, Xi'an 710054, China
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

The aim of this paper is to present some ways of constructing a lattice ordered effect algebra from the given family of MV-algebras. The loop lemma of lattice ordered effect algebras is proved. Then the definitions of Greechie diagrams of effect algebras are given. All these results have generalized those of orthomodular lattices. As applications of loop lemma and Greechie diagrams, some lattice ordered effect algebras without states are presented.