Hyper-commutators in effect algebras

被引：0
作者：
Ji, Wei [1 ]
Xie, Hai [1 ]
机构：
[1] Guilin Univ Technol, Coll Sci, Guilin 541004, Guangxi, Peoples R China
来源：
SOFT COMPUTING | 2019年 / 23卷 / 15期
基金：
中国国家自然科学基金;
关键词：
Effect algebra; Hyper-operation; Commutator; Torsion element; Sharp element;
D O I：
10.1007/s00500-018-3516-z
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The hyper-commutators in effect algebras as a generalization of commutators in lattice effect algebras are defined, and their properties are studied. We prove that a nonzero element is in some hyper-commutator if and only if it is a torsion element in effect algebras with the maximality property. Thus, homogeneity can be characterized by hyper-commutators. Some properties of Riesz ideals related to hyper-commutators are also studied. As an application, we prove that commutators are sharp in lattice effect algebras and every block-finite lattice effect algebra is commutator-finite.
引用
收藏
页码：5967 / 5973
页数：7
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