Commutative rings having only a finite number of ideals
The paper tries to describe all commutative rings with identity having only finitely many ideals. Obviously those rings are artinian, commutative artinian rings decompose into a direct sum of local rings. So the problem reduces to artinian rings. Their structure is well known. Proofs are provided for I. S. Cohen's structure theorems for local artinian rings (theorems 1 and 2). The proof of theorem 1 uses a ``polynomial'' version of Hensel's lemma (L 1).
scientific article; zbMATH DE number 3899039