B-separating algebras
type: Item
instance of: scholarly article
title: B-separating algebras
zbMATH Open document ID: 0623.08005
DOI: 10.1007/BF01988800
author: A. I. Omarov
published in: Algebra and Logic
publication date: 1986-01-01T00:00:00Z
review text: A universal algebra A is said to be B-separating if any isomorphism of its Boolean powers \(A[B_ 1]\) and \(A[B_ 2]\) implies \(B_ 1\cong B_ 2\). In this paper some problems of \textit{S. Burris} [Algebra Univers. 5, 341-360 (1975; Zbl 0328.08003)] are solved. In particular the following results are proved: 1) No Abelian group is B-separating; 2) If A is a finite B-separating algebra and A[B] is equationally compact then B is complete; 3) (GCH) If A[B] is k-saturated (k\(\geq \omega)\) then B is k- saturated; 4) If A is a finite B-separating algebra then \(A[B_ 1]\equiv A[B_ 2]\Rightarrow B_ 1\equiv B_ 2\) (elementary equivalence).
Mathematics Subject Classification ID: 08B25
Mathematics Subject Classification ID: 08A45
Mathematics Subject Classification ID: 03C50
Mathematics Subject Classification ID: 03C20
zbMATH DE Number: 4010584
zbMATH Keywords: universal algebra
zbMATH Keywords: isomorphism
zbMATH Keywords: Boolean powers
zbMATH Keywords: finite B-separating algebra
zbMATH Keywords: equationally compact
zbMATH Keywords: elementary equivalence
MaRDI profile type: Publication
cites work: Counting models in universal Horn classes
cites work: Boolean powers
description: scientific article; zbMATH DE number 4010584