Congruences and ideals in pseudo effect algebras as total algebras

被引：0
作者：
Silvia Pulmannová
Elena Vinceková
机构：
[1] Slovak Academy of Sciences,Mathematical Institute
来源：
Soft Computing | 2010年 / 14卷
关键词：
Pseudo-effect algebra; Ideal; Congruence; Commutative directoid;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Congruences and ideals in pseudo-effect algebras and their total algebra versions are studied. It is shown that every congruence of the total algebra induces a Riesz congruence in the corresponding pseudo-effect algebra. Conversely, to every normal Riesz ideal in a pseudo-effect algebra there is a total algebra, in which the given ideal induces a congruence of the total algebra. Ideals of total algebras corresponding to lattice-ordered pseudo-effect algebras are characterized, and it is shown that they coincide with normal Riesz ideals in the pseudo-effect algebras.
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页码：1209 / 1215
页数：6
相关论文
共 39 条
[1]  
Avallone A(2003)Congruences and ideals of effect algebras Order 20 67-77
[2]  
Vitolo P(2009)Many-valued quantum algebras Algebra Univers 63 63-90
[3]  
Chajda I(2009)Every effect algebra can be made into a total algebra Algebra Univers 61 139-150
[4]  
Halaš R(1958)Algebraic analysis of many valued logics Trans Am Math Soc 88 467-490
[5]  
Kühr J(2000)Some ideal lattices in partial Abelian monoids and effect algebras Order 17 72-92
[6]  
Chajda I(2001)Pseudo-effect algebras. I. Basic properties Int J Theor Phys 40 685-701
[7]  
Halaš R(2001)Congruences and states on pseudo-effect algebras Found Phys Lett 14 422-446
[8]  
Kühr J(1994)Effect algebras and unsharp quantum logics Found Phys 24 1331-1352
[9]  
Chang CC(1996)Quantum MV-algebras Studia Logica 56 303-417
[10]  
Chevalier G(1989)Toward a formal language for unsharp properties Found Phys 19 931-945
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