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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- passes to quotient rings

- stable under products (Counterexample: $R_{ 57 }$)
- forms an equational class (counterexample needed)
- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)

Rings

Legend

- = has the property
- = does not have the property
- = information not in database