On the sum of a direct system of universal algebras with nullary polynomials
type: Item
instance of: scholarly article
title: On the sum of a direct system of universal algebras with nullary polynomials
zbMATH Open document ID: 0548.08001
DOI: 10.1007/BF01190429
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: In the presence of nullary operations, the sum of a direct system of universal algebras in the sense of the author's earlier paper [Fundam. Math. 61, 183-189 (1967; Zbl 0168.267)] can be formed when the direct system contains a smallest member. Various theorems from the above and another paper of the author [ibid. 64, 241-247 (1969; Zbl 0187.287)] remain valid for the extended sum concept, e.g.: An equation holds in a nontrivial sum iff it is regular and holds in each summand. If K is an equational class such that an equation of the form \(x\cdot y=x\) holds in K, then any algebra satisfying all regular equations that hold in K is the sum of a direct system of algebras from K.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08B25
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 03C05
zbMATH DE Number: 3873398
zbMATH Keywords: nullary operations
zbMATH Keywords: direct system of universal algebras
zbMATH Keywords: extended sum
zbMATH Keywords: regular equations
author: Jerzy Płonka
reviewed by: Manfred Armbrust
MaRDI profile type: Publication
cites work: A generalization of Płonka sums
cites work: On classes of algebras definable by regular equations
cites work: Subdirect decomposition of Plonka sums
cites work: On a representation of groupoids as sums of directed systems
cites work: On a method of construction of abstract algebras
cites work: On equational classes of abstract algebras defined by regular equations
cites work: On sums of direct systems of Boolean algebras
cites work: Q4145751
full work available at URL: https://doi.org/10.1007/bf01190429
OpenAlex ID: W2074057233
description: scientific article; zbMATH DE number 3873398