Credits: 7,5

Type: bridging

Objectives:

To provide an introduction to the basic concepts of commutative algebra, giving special attention to the affine algebras of number fields and their integer rings, which are of particular interest in algebraic geometry and number theory.

Knowledge:

• Modules. Fraction rings and primary decomposition.
• Noetherian rings. Systems of algebraic equations.
• Integer elements. Dedekind rings and valuation rings.
• Dimension theory.

Subject-specific competences:

• To develop use of the basic tools of commutative algebra sufficient to be able to demonstrate and comprehend Hilbert's zeros theorem.
• To handle the basic vocabulary of affine algebra and geometry.