A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R is that the subset R - m is precisely the set of ring units, where m is the maximal ideal. This follows because, in a ring, any nonunit belongs to at least one maximal ideal.

Jacobson radical | localization | maximal ideal | quasilocal ring | regular local ring | residue field | ring unit | semilocal ring