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Commutative algebra Description

Key Elements

Code

MATH 405

Formation

M1 Mathematics

Semester

2

Credits

6

Number of Teaching Hours

36

Number of Tutoring Sessions

24

Number of Laboratory Sessions

0

This course is optional

Content

Objective

Content

• Modules of homomorphisms, injective and projective modules, tensor product and flat modules. • Prime and maximal ideals in a ring, operation over ideals. Chinese remainder theorem, nilradical and Jacobon’s radical; divisibility in a ring, factorial ring, primary ideals and primary decomposition. • rings and modules of fractions. Ideals in a ring of fractions, local ring. • Integral and almost integral elements over a ring. Integrally closed and almost integrally closed rings, Dedekind rings, fractional ideals, ideals classes.