ABSTRACT
The birth of algebraic number theory took place while attempts were made to prove Fermat’s Last Theorem during the 18th century and early 19th century. The creation of ideals had a bearing on the growth of ring theory. Ideals were used long before homomorphisms reached the scene. There was a shift of emphasis from ideals to homomorphisms. This was brought about by a German mathematician Emmy Noether (1882–1935). Her view of ring theory has had a tremendous inuence on the growth of ring theory. Van der Waerden’s (1903–1996) Modern Algebra published in 1931 gave the modern view of algebra as he drew the theorems and their applications from the courses presented by E. Artin and Emmy Noether, which he had attended at Gottingen. The class of rings which Emmy Noether had investigated is known as the class of Noetherian rings in honour of the great woman algebraist Emmy Noether. Among Noetherian rings are the ring of integers and rings of polynomials.
