齐次效应代数的黏合构造
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摘要
本文给出了一些用一族具有Riesz分解性质的效应代数黏合成齐次的效应代数的条件,并研究了通过线性MV-代数替换正交代数中的原子得到只含有1型原子的有限的齐次效应代数的方法。
In this paper,we present some sufficient conditions for pasting a homogeneous effect algebra using a family of effect algebras with the Riesz decomposition property. Then, a kind of condition under which we can get a finite homogeneous effect algebra without atoms of type of 2 by substituting the atoms of an orthoalgebra with some linear MV-effect algebras is provided.
In this paper,we present some sufficient conditions for pasting a homogeneous effect algebra using a family of effect algebras with the Riesz decomposition property. Then, a kind of condition under which we can get a finite homogeneous effect algebra without atoms of type of 2 by substituting the atoms of an orthoalgebra with some linear MV-effect algebras is provided.
引文
[1] Foulis D J,Bennett M K.Effect algebras and unsharp quantum logics[J].Foundations of Physics,1994,24(10):1331～1352.
[2] 李永明.标度广义效应代数和标度效应代数的结构[J].数学学报,2008,51(5):863～876.
[3] 周湘南.理论的相容度及效应代数的滤子与商[D].陕西师范大学,2005.
[4] 尚云.量子逻辑中有效代数与伪有效代数的研究[D].陕西师范大学,2005.
[5] Jen■a G,Rie■anová Z.On sharp elements in lattice ordered effect algebras[J].Busefal,1999,80:24～29.
[6] Dvure■enskij A,Pulmannová S.New trends in quantum structures[M].Kluwer Academic Publishers,2000.
[7] Jen■a G.Blocks of homogeneous effect algebras[J].Bulletin of the Australian Mathematical Society,2001,64(1):81～98.
[8] Navara M,Rogalewicz V.The pasting constructions for orthomodular posets[J].Mathematische Nachrichten,1991,154:157～168.
[9] Xie Y J,Li Y M,Yang A L.The pasting constructions of lattice ordered effect algebras[J].Information Sciences,2010,180(12):2476～2486.
[10] Xie Y J,Li Y M,Yang A L.The pasting constructions for effect algebras[J].Mathematica Slovaca,2014,64(5):1051～1074.
[11] 颉永建.效应代数与伪效应代数的结构[M].北京:科学出版社,2017.
[12] Dvure■enskij A.Central elements and Cantor-Bernstein’s theorem for pseudo-effect algebras[J].Journal of the Australian Mathematical Society,2003,74:121～143.
[13] Xie Y J,Li Y M,Yang A L.Pasting of lattice-ordered effect algebras[J].Fuzzy Sets and Systems,2015,260:77～96.
[14] Bennett M K,Foulis D J.Phi-symmetric effect algebras[J].Foundations of Physics,1995,25(12):1699～1722.
[15] Dvure■enskij A,Xie Y J.Atomic effect algebras with the Riesz decomposition property[J].Foundations of Physics,2012,42(8):1078～1093.
[16] Paseka J,Rie■anová Z.Isomorphism theorems on generalized effect algebras based on atoms[J].Information Sciences,2009,179(5):521～528.
[2] 李永明.标度广义效应代数和标度效应代数的结构[J].数学学报,2008,51(5):863～876.
[3] 周湘南.理论的相容度及效应代数的滤子与商[D].陕西师范大学,2005.
[4] 尚云.量子逻辑中有效代数与伪有效代数的研究[D].陕西师范大学,2005.
[5] Jen■a G,Rie■anová Z.On sharp elements in lattice ordered effect algebras[J].Busefal,1999,80:24～29.
[6] Dvure■enskij A,Pulmannová S.New trends in quantum structures[M].Kluwer Academic Publishers,2000.
[7] Jen■a G.Blocks of homogeneous effect algebras[J].Bulletin of the Australian Mathematical Society,2001,64(1):81～98.
[8] Navara M,Rogalewicz V.The pasting constructions for orthomodular posets[J].Mathematische Nachrichten,1991,154:157～168.
[9] Xie Y J,Li Y M,Yang A L.The pasting constructions of lattice ordered effect algebras[J].Information Sciences,2010,180(12):2476～2486.
[10] Xie Y J,Li Y M,Yang A L.The pasting constructions for effect algebras[J].Mathematica Slovaca,2014,64(5):1051～1074.
[11] 颉永建.效应代数与伪效应代数的结构[M].北京:科学出版社,2017.
[12] Dvure■enskij A.Central elements and Cantor-Bernstein’s theorem for pseudo-effect algebras[J].Journal of the Australian Mathematical Society,2003,74:121～143.
[13] Xie Y J,Li Y M,Yang A L.Pasting of lattice-ordered effect algebras[J].Fuzzy Sets and Systems,2015,260:77～96.
[14] Bennett M K,Foulis D J.Phi-symmetric effect algebras[J].Foundations of Physics,1995,25(12):1699～1722.
[15] Dvure■enskij A,Xie Y J.Atomic effect algebras with the Riesz decomposition property[J].Foundations of Physics,2012,42(8):1078～1093.
[16] Paseka J,Rie■anová Z.Isomorphism theorems on generalized effect algebras based on atoms[J].Information Sciences,2009,179(5):521～528.