Verbal subalgebra

This article is about a property that can be evaluated for a subalgebra in an algebra with specified operations, where algebra is used in the universal algebra sense.
View more such properties

Definition

In analogy with verbal subgroup. PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.

Particular cases

Variety of interest	Characteristic subalgebra in that variety	Facts peculiar to characteristic subalgebras in that variety
variety of groups, with the usual universal algebra axiomatization of groups	verbal subgroup	on account of characteristic subalgebras are ideals in the variety of groups, these are normal subgroups and we can consider the corresponding quotient groups
variety of Lie rings, with the usual universal algebra axiomatization of Lie rings	verbal Lie subring

Relation with other properties

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
fully invariant subalgebra	invariant under all endomorphisms			|FULL LIST, MORE INFO
characteristic subalgebra	invariant under all automorphisms			|FULL LIST, MORE INFO