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

页码：5967 / 5973

页数：7

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