Ideals and filters in pseudo-effect algebras
type: Item
instance of: scholarly article
title: Ideals and filters in pseudo-effect algebras
zbMATH Open document ID: 1073.81010
author: Junde Wu
author: Shijie Lu
author: Zhi-Hao Ma
published in: International Journal of Theoretical Physics
publication date: 2005-03-15T00:00:00Z
review text: In his thesis of 2003, Jing proved that, in a pseudo-effect algebra, an ideal is always a local ideal and that a filter is always a local filter. On the other hand, \textit{Y. Shang} and \textit{Y. Li} introduced in [Int. J. Theor. Phys. 42, No. 12, 2823--2829 (2003; Zbl 1037.81007)] the notion of a generalized ideal and proved that it is equivalent to the notion of an ideal. In the paper under review, the authors show that, just as in effect algebras, every local ideal (local filter) in a pseudo-effect algebra is an ideal (resp., filter) and that the notions of generalized ideal and ideal are equivalent also in pseudo-effect algebras. Their methods rest on the left and right subtraction operations on pseudo-effect algebras introduced by them in a recent paper [Int. J. Theor. Phys. 43, No. 6, 1453--1460 (2004; Zbl 1073.81011), reviewed below].
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 2146155
zbMATH Keywords: filter
zbMATH Keywords: generalized ideal
zbMATH Keywords: ideal
zbMATH Keywords: local filter
zbMATH Keywords: local ideal
zbMATH Keywords: pseudo-effect algebras
MaRDI profile type: Publication
full work available at URL: b:ijtp.0000048628.89053.de
OpenAlex ID: W2076198472
DOI: 10.1023/B:IJTP.0000048628.89053.DE
description: scientific article; zbMATH DE number 2146155