Erhard Aichinger, Peter Mayr,
"Finitely generated equational classes"
, in Journal of Pure and Applied Algebra, Vol. 220, Seite(n) 2816-2827, 2016, ISSN: 0022-4049
Original Titel:
Finitely generated equational classes
Sprache des Titels:
Englisch
Original Kurzfassung:
Classes of algebraic structures that are defined by equational laws are called \emph{varieties}
or \emph{equational classes}.
A variety is finitely generated if it is defined by the
laws that hold in some fixed finite algebra.
We show that
every subvariety of a finitely generated congruence permutable
variety is finitely generated; in fact, we prove the
more general result that
if a finitely generated variety has an edge term,
then all its subvarieties are finitely generated as well.
This applies in particular to
all varieties of groups, loops, quasigroups and their expansions
(e.g., modules, rings, Lie algebras, \dots).
Forschungs-