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On derived varieties

  • Derived varieties play an essential role in the theory of hyperidentities. In [11] we have shown that derivation diagrams are a useful tool in the analysis of derived algebras and varieties. In this paper this tool is developed further in order to use it for algebraic constructions of derived algebras. Especially the operator \(S\) of subalgebras, \(H\) of homomorphic irnages and \(P\) of direct products are studied. Derived groupoids from the groupoid \(N or (x,y)\) = \(x'\wedge y'\) and from abelian groups are considered. The latter class serves as an example for fluid algebras and varieties. A fluid variety \(V\) has no derived variety as a subvariety and is introduced as a counterpart for solid varieties. Finally we use a property of the commutator of derived algebras in order to show that solvability and nilpotency are preserved under derivation.

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Metadaten
Author:Dietmar Schweigert
URN (permanent link):urn:nbn:de:hbz:386-kluedo-50592
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (285)
Document Type:Report
Language of publication:English
Publication Date:2017/11/10
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/10
Number of page:10
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)