On subtractive varieties. IV: Definability of principal ideals
type: Item
instance of: scholarly article
title: On subtractive varieties. IV: Definability of principal ideals
zbMATH Open document ID: 0934.08002
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
review text: [For parts I--III see Zbl 0799.08010, Zbl 0902.08010 and Zbl 0906.08005, respectively.] The concept of ideal in universal algebra was introduced by the second author. This paper deals with equationally definable principal ideals (EDPI) in the so-called subtractive varieties (alias varieties permutable at 0). The authors introduce one variety of generalized Hilbert algebras and prove that this is a paradigm of a subtractive variety with EDPI. Then they deal with principal ideal operations and with the cases of meet and join of principal ideals being equationally definable.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 1407081
zbMATH Keywords: ideal
zbMATH Keywords: subtractive variety
zbMATH Keywords: equationally definable principal ideals
zbMATH Keywords: generalized Hilbert algebras
author: Paolo Agliano
author: Aldo Ursini
MaRDI profile type: Publication
full work available at URL: s000120050059
OpenAlex ID: W2064612152
DOI: 10.1007/S000120050059
description: scientific article; zbMATH DE number 1407081