A Noetherian ring is a type of ring in abstract algebra that satisfies the ascending chain condition on ideals. This means that any increasing sequence of ideals eventually stabilizes, or in simpler terms, there are no infinitely increasing chains of ideals. This property ensures that every ideal in a Noetherian ring is finitely generated, which is a crucial aspect in many areas of mathematics. Noetherian rings are named after the mathematician Emmy Noether, who made significant contributions to algebra. These rings play a vital role in various fields, including algebraic geometry and commutative algebra, as they provide a framework for understanding the structure of rings and their ideals.