In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal element in the poset of proper right ideals, and similarly, a maximal left ideal is defined to be a maximal element of the poset of proper left ideals. Since a one sided maximal ideal "A" is not necessarily two-sided, the quotient "R"/"A" is not necessarily a ring, but it is a simple module over "R". If "R" has a unique maximal right ideal, then "R" is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J("R").