Generalized local ring

Symbol-free definition
A positively graded commutative unital ring R is termed a generalized local ring if its degree 0 part is local and Noetherian, and R is a finitely generated as an algebra over its degree 0 part.

Uniqueness of maximal ideal
A generalized local ring has a unique maximal homogeneous ideal.

Stronger properties

 * Multivariate polynomial ring over a field