# Property: Henselian local

Definition: A commutative local ring in which Hensel's Lemma holds. (For any monic polynomial $p$ in $R[x]$, all factorizations in $(R/M)[x]$ into a product of coprime monic polynomials lift to factorizations in $R[x]$.)

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## Metaproperties:

This property has the following metaproperties
• passes to quotient rings