In: Mathematica Slovaca, vol. 64, no. 5
Yongjian Xie - Yongming Li - Aili Yang
Rok, strany: 2014, 1051 - 1074
lattice-ordered effect algebra, block, MV-effect algebra, pasting, Greechie diagram
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.
Xie, Y., Li, Y., Yang, A. 2014. The pasting constructions for effect algebras. In Mathematica Slovaca, vol. 64, no.5, pp. 1051-1074. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0258-y
Xie, Y., Li, Y., Yang, A. (2014). The pasting constructions for effect algebras. Mathematica Slovaca, 64(5), 1051-1074. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0258-y
Publikované: 1. 10. 2014