Commutative Algebra

In general Algebra, the commutative algebra is the branch of mathematics which studies the commutative rings, their ideal, the Module S and the algebras. It is fundamental for the algebraic Géométrie and the Algebraic theory of the numbers.

David Hilbert is regarded as the true founder of this discipline called initially the “theory of the ideals”. Many supposes that he would have thought this theory like an approach aiming at replacing the theory of the complex functions. The calculative aspect was presented like secondary by leaving a greater place to the structures. The study of the Module S, attached later to this theory under the influence of Emmy Noether, presents in a certain form the work of Kronecker, and is a technical improvement exempting always to work directly on the particular case of the ideals.

Compared to the concept of diagram, the commutative algebra can be regarded as being the local theory or the theory closely connected of the algebraic Géométrie.

The general study of the rings which are not supposed to be commutative is known under the name of noncommutative Algèbre; it is prolonged by the Théorie of the rings, by the Théorie of the representation and by other fields like that of the theory of the algebras of Banach.

To have other bonds see, the Liste of the articles of commutative algebra.

Random links: