Characteristicity is transitive for any variety of algebras
ANALOGY: This is an analogue in variety of algebrass of a fact encountered in group. The old fact is: characteristicity is transitive.
View other analogues of characteristicity is transitive|View other analogues from group to variety of algebras (OR, View as a tabulated list)
Suppose is a variety of algebras. Suppose is an algebra of , is a subalgebra of that is characteristic in (i.e., every automorphism of sends to itself) and is a subalgebra of that is characteristic in . Then, is a characteristic subalgebra of .
Other similar facts
- Full invariance is transitive for any variety of algebras
- Derivation-invariance is transitive for any subvariety of the variety of rings
- Derivation-invariance is transitive for Lie rings