Residuated lattices and lattice effect algebras
type: Item
instance of: scholarly article
title: Residuated lattices and lattice effect algebras
zbMATH Open document ID: 1122.81016
author: Xiangnan Zhou
author: Qingguo Li
author: Guojun Wang
published in: Fuzzy Sets and Systems
publication date: 2007-05-04T00:00:00Z
review text: The authors study two partial operations in effect algebras, namely \(a \odot b = (a' \oplus b')'\) if \(a' \oplus b'\) is defined and \(a \to_p b = a' \oplus b\) if \(a' \oplus b\) is defined. They show, e.g., that for an effect algebra \((E, \oplus, 0, 1)\) we obtain a (dual) effect algebra \((E, \odot,0,1)\). Using these operations they construct an adjoint pair in an effect algebra with the Riesz decomposition property to obtain an involutive residuated lattice. On the other hand, they prove that an involutive residuated lattice \((L, \leq \otimes, \to, 0, 1)\) corresponds to an effect algebra with the Riesz decomposition property if and only if \(a \land b = a \otimes (a \to b)\) for every \(a,b \in L\).
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 5149487
zbMATH Keywords: lattice effect algebra
zbMATH Keywords: involutive residuated lattice
zbMATH Keywords: Riesz decomposition property
reviewed by: Josef Tkadlec
MaRDI profile type: Publication
full work available at URL: j.fss.2006.12.014
OpenAlex ID: W1968222062
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DOI: 10.1016/J.FSS.2006.12.014
description: scientific article; zbMATH DE number 5149487