On P-dominions of continuous algebras
type: Item
instance of: scholarly article
title: On P-dominions of continuous algebras
zbMATH Open document ID: 0594.08006
DOI: 10.1016/0022-4049(86)90113-1
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: For each subset system Z and each, possibly infinitary, type of algebras, a sufficient condition is presented for a Z-continuous homomorphism \(f: A\to B\) to be an epi. This is related to the problem whether, for a given Z-continuous algebra A, the cardinality of B is bounded (i.e., whether the category of Z-continuous algebras is co-wellpowered) investigated by the reviewer and \textit{V. Koubek}, \textit{E. Nelson} and \textit{J. Reiterman} [Trans. Am. Math. Soc. 291, 681-699 (1985; Zbl 0578.08005)]. The answer is negative for infinitary algebras in case \(Z=all\) countably directed subsets.
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 08A65
Mathematics Subject Classification ID: 08A35
zbMATH DE Number: 3954994
zbMATH Keywords: subset system
zbMATH Keywords: Z-continuous homomorphism
zbMATH Keywords: Z-continuous algebra
zbMATH Keywords: category of Z-continuous algebras
zbMATH Keywords: infinitary algebras
author: Ana Pasztor
reviewed by: Jiří Adámek
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90113-1
OpenAlex ID: W2013723877
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description: scientific article; zbMATH DE number 3954994