Notes on \(R1\)-ideals in partial abelian monoids
type: Item
instance of: scholarly article
title: Notes on \(R1\)-ideals in partial abelian monoids
zbMATH Open document ID: 1011.06017
author: Gejza Jenča
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: A cancellative positive partial abelian monoid (CPAM) is an algebra \(\mathcal P =(P;\oplus ,0)\) of type \((2,0)\) which is a partial commutative monoid satisfying the left cancellation law and \(a\oplus b=0\) implies \(a=0\). The author generalizes effect algebras or \(D\)-posets. Several concepts of ideals are introduced. Especially, an \(R1\)-ideal \(I\) is defined in such way that, for each CPAM \(\mathcal P\), \(\mathcal P /I\) is also a CPAM. The author studies congruences on CPAM associated with \(R1\)-ideals and the lattice of all \(R1\)-ideals on a CPAM. An \(R1\)-ideal satisfying one more condition is called a Riesz ideal, the lattice of all Riesz ideals is a sublattice of the lattice of all ideals as shown by the author.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 1899941
zbMATH Keywords: partial monoid
zbMATH Keywords: effect algebra
zbMATH Keywords: ideal
zbMATH Keywords: Riesz ideal
MaRDI profile type: Publication
full work available at URL: s000120050161
OpenAlex ID: W2306992649
DOI: 10.1007/S000120050161
description: scientific article; zbMATH DE number 1899941