To deepen the study of algebraic structures such as groups, rings and modules. This will be applied to the study of the canonical forms of matrices, and to the classification of finite abelian groups,.
Course Prerequisites
The content of the courses Linear Algebra and Algebra 1
Teaching Methods
Lessons and exercises
Assessment Methods
Written test (problems and open questions on the theory, 2 hours) and oral examination.
Contents
After a first part which deals with quotients of vector spaces, the course focuses on the study of algebraic structures endowed with two operations: rings, algebras, modules, and fields. Program. - Linear algebra: quotients and morphisms of vector spaces - Rings: definitions and basic results, examples, substructures, ideals, quotients and morphisms. - Commutative rings: irreducible and prime elements, Chinese remainder Theorem, UFDs and PIDs, polynomial rings and factorization. - Fields and extensions (basic definitions and examples). - Modules: definitions and basic results. - Classifications of finitely generated modules on PIDs, finitely generated abelian groups, Jordan canonical form, Cayley-Hamilton Theorem.
Course Language
Italian
More information
The reception with the teacher is by appointment: contact at claudio.quadrellił@uninsubria.it
