Geometric and conditional geometric equivalences of algebras
type: Item
instance of: scholarly article
title: Geometric and conditional geometric equivalences of algebras
zbMATH Open document ID: 1284.08004
author: A. G. Pinus
published in: Algebra and Logic
publication date: 2013-07-19T00:00:00Z
review text: Two universal algebras are said to be geometrically equivalent (conditionally geometrically equivalent) if pairs of different systems of termal equations (of quantifier-free elementary formulas) defining common algebraic sets (definable subsets) are properly the same. An algebra \(A\) is called uniformly locally finite if there exists a function \(h:\omega\to\omega\) such that for any \(n\in\omega\) and any \(B\subseteq A\) the inequality \(|B|\leq n\) entails for the subalgebra \((B)_A\) of \(A\) generated by the set \(B\) the equality \(|(B)_A|\leq h(n)\). The main result of the paper states that for any uniformly locally finite algebras \(A_1\) and \(A_2\) of finite signature the following conditions are equivalent: (a) \(A_1\) and \(A_2\) are geometrically equivalent; (b) for any infinite Boolean algebra \(B\) the \(B\)-powers of \(A_1\) and \(A_2\) are conditionally geometrically equivalent.
Mathematics Subject Classification ID: 08A05
zbMATH DE Number: 6189469
zbMATH Keywords: geometrically equivalent algebras
zbMATH Keywords: conditionally geometrically equivalent algebras
zbMATH Keywords: syntactically implicitly equivalent algebras
zbMATH Keywords: \(\infty\)-quasiequational theory of algebras
reviewed by: V. N. Saliĭ
MaRDI profile type: Publication
full work available at URL: s10469-013-9210-4
OpenAlex ID: W2026164989
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DOI: 10.1007/S10469-013-9210-4
description: scientific article; zbMATH DE number 6189469