\(L\)-algebras in logic, algebra, geometry, and topology
type: Item
instance of: scholarly article
title: \(L\)-algebras in logic, algebra, geometry, and topology
zbMATH Open document ID: 1457.03076
author: Wolfgang Rump
published in: Soft Computing
publication date: 2020-07-16T00:00:00Z
review text: \(L\)-algebras are treated here mainly from the viewpoint of algebraic logic as algebras of kind \((A,\to,1)\) satisfying the axioms \((x \to y) \to (x \to z) = (y \to x) \to (y \to z)\) and \(x \to y = y \to x = 1 \Rightarrow x = y\), cf. [the author, J. Algebra 320, No. 6, 2328--2348 (2008; Zbl 1158.06009)]. The paper is an informal review of \(L\)-algebras, their examples from, and applications in, logic, arithmetics, algebra, analysis, geometry, topology. In particular, discussed are connections of these algebras with hoops and Heyting algebras, and also their relationship to \(\ell\)-groups.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 54B05
zbMATH DE Number: 7221933
zbMATH Keywords: algebraic logic
zbMATH Keywords: \(L\)-algebra
zbMATH Keywords: \( \ell \)-group
zbMATH Keywords: hoop
zbMATH Keywords: \(p\)-adic numbers
zbMATH Keywords: projective space
zbMATH Keywords: measure
zbMATH Keywords: integration
zbMATH Keywords: Heyting algebra
MaRDI profile type: Publication
full work available at URL: s00500-019-04616-w
OpenAlex ID: W3000511167
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DOI: 10.1007/S00500-019-04616-W
description: scientific article; zbMATH DE number 7221933