A note of filters in effect algebras.
type: Item
instance of: scholarly article
title: A note of filters in effect algebras.
zbMATH Open document ID: 1325.06015
DOI: 10.1155/2013/570496
author: Biao Long Meng
author: Xiaolong Xin
published in: Chinese Journal of Mathematics
publication date: 2014-10-16T00:00:00Z
review text: Summary: We investigate relations of the two classes of filters in effect algebras (resp., MV-algebras). We prove that a lattice filter in a lattice ordered effect algebra (resp., MV-algebra) \(E\) does not need to be an effect algebra filter (resp., MV-filter). In general, in MV-algebras, every MV-filter is also a lattice filter. Every lattice filter in a lattice ordered effect algebra \(E\) is an effect algebra filter if and only if \(E\) is an orthomodular lattice. Every lattice filter in an MV-algebra \(E\) is an MV-filter if and only if \(E\) is a Boolean algebra.
Mathematics Subject Classification ID: 06F35
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 6356623
zbMATH Keywords: lattice ordered effect algebras
zbMATH Keywords: MV-algebras
zbMATH Keywords: lattice filters
zbMATH Keywords: effect algebra filters
Wikidata QID: Q58920748
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/570496
OpenAlex ID: W1972567339
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description: scientific article; zbMATH DE number 6356623