Module MA3412: Abstract algebra II

Credit weighting (ECTS)

5 credits

Semester/term taught

Hilary term 2013-14

Contact Hours

11 weeks, 3 lectures including tutorials per week

Lecturer

Prof. David Wilkins

Learning Outcomes

On successful completion of this module, students will be able to

Justify with reasoned logical argument basic properties of Noetherian modules and finite field extensions.
Justify with reasoned logical argument results concerning the structure of finitely-generated modules over integral domains and principal ideal domains.
Describe and justify with reasoned logical argument basic properties of algebraic integers.

Module Content

The module will cover the following topics:

Factorization in Integral Domains. Principal Ideal Domains.
Basic properties of modules over unital commutative rings. Noetherian modules. Noetherian rings. Hilbert's Basis Theorem.
Linear independence and free modules. Free modules over integral domains. Torsion modules. Free modules of finite rank over principal ideal domains. Torsion-free modules. The classification theorem for finitely-generated modules over principal ideal domains. The Jordan Normal Form.
Algebraic numbers and algebraic integers.

Lecture notes, problems, worked solutions to selected past examination questions and further information relevant to the module are available from the module webpage at http://www.maths.tcd.ie/~dwilkins/Courses/MA3412/.

Module Prerequisite