[[Algebra theory MOC]]
# Quotient algebra

Given a two-sided [[Algebra ideal|ideal]] $I \leq A$ of an [[K-algebra|algebra]] $(A,*)$ over a field $\mathbb{K}$, the **quotient algebra** $A / I$ is the [[Zen/Quotient vector space]] with the well-defined product #m/def/falg 
$$
\begin{align*}
(a + I) * (b+I) = a *b + I
\end{align*}
$$

## Special cases

- [[Quotient Lie algebra]]

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