The Cauchy equation on \(l\)-semigroups
type: Item
instance of: scholarly article
title: The Cauchy equation on \(l\)-semigroups
zbMATH Open document ID: 1004.39012
author: P. Benvenuti
author: D. Vivona
author: Maria Divari
published in: Aequationes Mathematicae
publication date: 2002-06-27T00:00:00Z
review text: A binary operation \(\oplus: [0,M]^2 \to[0,M]\) is called a pseudo-addition if the following properties are satisfied: commutativity, associativity, 0 is the neutral element, monotonicity i.e. \(x\leq x'\), \(y\leq y' \Rightarrow x\oplus y\leq x'\oplus y'\) and continuity i.e. \(x_n\to x\), \(y_n\to y \Rightarrow x_n\oplus y_n\to x\oplus y\). the pair \(([0,M], \oplus)\) is an \(l\)-semigroup. The authors give the general solution of the Cauchy equation on a general \(l\)-semigroup. Then they present some examples of solutions.
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1761055
zbMATH Keywords: \(l\)-semigroups
zbMATH Keywords: general solution
zbMATH Keywords: Cauchy equation
reviewed by: Ilie Corovei
MaRDI profile type: Publication
full work available at URL: s00010-002-8020-x
OpenAlex ID: W1976855678
DOI: 10.1007/S00010-002-8020-X
description: scientific article; zbMATH DE number 1761055