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SF2706 Algebra 7.5 credits

Administer About course

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus SF2706 (Autumn 2007–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Polynomial rings, modules, tensor product, modules over PID, field extensions.

Intended learning outcomes

The goal of the course is to make the student familiar with the basic concepts of polynomial rings, modules and field extensions.

This means in particular that the student, after completing the course, will

  • Know the concepts of polynomial rings, ideals and irreducible polynomials
  • Have knowledge of when polynomial rings are UFD.
  • Be able to use Eisensteins irreducibility criteria
  • Know the concepts of modules, submodules and quotients.
  • Know the concepts of direct sum, tensor product, exact sequences,
  • Recognize the concepts of projective modules, injective modules, flat modules and Hom-functors.
  • Be familiar with the construction and the universal properties of tensor algebras, symmetric algebras, and exterior algebras
  • Know the structure theorem for finitely generated modules over PID.
  • Understand how linear algebra can be pursued over rings,
  • Know the rational canonical form and the Jordan form for matrices
  • Know the concepts of field extensions, algebraic extension, minimal polynom
  • Know the concepts of splitting fields, closures, separable and inseparable extensions, cyclotomic polynomials.

Literature and preparations

Specific prerequisites

SF2703 or equivalent.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

Abstract Algebra by D.S. Dummit and R.M. Foote.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F

Examination

  • TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

Written exam, and home work assignments.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

No information inserted

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

SCI/Mathematics

Main field of study

Mathematics

Education cycle

Second cycle

Add-on studies

No information inserted