The pasting constructions for effect algebras-Reference-Cited by-同舟云学术

The pasting constructions for effect algebras

Published:2014-10-01 Issue:5 Volume:64 Page:1051-1074
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Xie Yongjan,Li Yongming¹,Yang Aili²

Affiliation:

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

2. College of Science, Xi’an University of Science and Technology, Xi’an, 710054, China

Abstract

Abstract The aim of this paper is to present several techniques of constructing a lattice-ordered effect algebra from a given family of lattice-ordered effect algebras, and to study the structure of finite lattice-ordered effect algebras. Firstly, we prove that any finite MV-effect algebra can be obtained by substituting the atoms of some Boolean algebra by linear MV-effect algebras. Then some conditions which can guarantee that the pasting of a family of effect algebras is an effect algebra are provided. At last, we prove that any finite lattice-ordered effect algebra E without atoms of type 2 can be obtained by substituting the atoms of some orthomodular lattice by linear MV-effect algebras. Furthermore, we give a way how to paste a lattice-ordered effect algebra from the family of MV-effect algebras.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.2478/s12175-014-0258-y.pdf

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1. A Geometric Approach to MV-Algebras;On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory;2016

2. Pasting of lattice-ordered effect algebras;Fuzzy Sets and Systems;2015-02