= Almost commutative algebra
{title2=$\operatorname{gr}A\text{ is commutative and finitely generated}$}
An almost commutative algebra over a <field> is an <algebra> with an exhaustive increasing nonnegative multiplicative <filtration> whose <associated graded ring> is commutative and finitely generated as an algebra over the field. A common presentation uses finitely many degree-one generators, scalar degree-zero part, and <commutators> that lower degree. The finite-generation requirement is essential: an infinitely generated commutative <polynomial ring> has commutative associated graded algebra but need not be <Noetherian>.
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