Algebra theory MOC

Algebra ideal

A -submodule¹ of a -algebra called a left-ideal iff , a right-ideal iff , and a two-sided ideal (sometimes just ideal) iff both conditions hold,² #m/def/ralg i.e. a left-ideal absorbs elements placed on the left, &c.

For an associatie algebra (in particular -monoid) ideal of a rng.
Given a two-sided ideal one may construct a quotient algebra .

Special cases

Lie algebra ideal

#state/tidy | #lang/en | #SemBr

Note that any vector subspace satisfying the definition is automatically a subalgebra. ↩
1988. Vertex operator algebras and the Monster, §1.3, p. 6 ↩