A local ring is a commutative ring 
with multiplicative
identity that contains a single maximal ideal.
In this case, the Jacobson radical equals this
maximal ideal.
One property of a local ring 
is that the subset 
is precisely the set of ring
units, where 
is the maximal ideal. This follows because, in a
commutative ring with multiplicative
identity, any element that is not a ring
unit belongs to at least one maximal ideal (Atiyah
and Macdonald 1969, p. 4).
