An Artinian ring is a type of ring in abstract algebra that satisfies the descending chain condition on ideals. This means that any descending sequence of ideals eventually stabilizes, meaning it cannot continue to decrease indefinitely. Artinian rings are important in the study of ring theory and have applications in various areas of mathematics. One key property of Artinian rings is that they are Noetherian, which means they also satisfy the ascending chain condition on ideals. This duality makes them particularly interesting in the context of commutative algebra and module theory. Examples of Artinian rings include finite-dimensional algebras over a field and certain matrix rings.