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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
Either Fields, Rings and Modules (MA2215) or Abstract Algebra I (MA3411).
Assessment Detail
This module will be examined in a 2-hour examination in Trinity term. There is no continuous assessment.