MVE150 / MMG500 Algebra

MVE150 / MMG500 Algebra

NEW !!  I have now posted six exams from 2020-2021 with solutions on Canvas as well as solutions to the six exams from 2017-2018 below.


This page contains the program of the course: lectures and exercise sessions. (Please read also the announcements on Canvas !)

Lecturer and examiner: Per Salberger.


The schedule of the course is in TimeEdit. Note that there have been changes due to spread of covid 19, 


The lectures will take place Tuesday 8-10 and Tuesday 10-12. The first Thursday January 20th there is also a lecture 13-15. All lectures will be on Zoom due to the spread of covid 19. I will send you the Zoom-link on Canvas.

The lectures are based on the same sections in Durbin's book as the recommened exercises below.


J.R. Durbin: Modern Algebra, An Introduction, John Wiley & Sons, version 5 or 6.

Note that the sections 53, 54, 55 in the fifth edition are moved to sections 56, 57, 58 in the sixth edition!


Problem sessions The problem sessions are held on Campus Thursday 13-15 and Friday 10-12, beginning January 21st. The problems will be chosen from the list of recommended exercises on the home page. All these are important, and more than half of them will be discussed during the problem sessions.

There will be two groups, both in English. You do NOT have the right to choose group yourself as the groups must be equally large due to the rapid spread of covid 19. The divison into groups is as follows.

Students with family names on A-L :  Group leader Douglas Molin , location EL42.

Students with family names on M-Ö :  Group leader Per Salberger , location MVH12.


Recommended exercises

The exercises below are selected from the sixth edition of Durbin’s book . The same exercises may also be found in the fifth edition and usually with the same numerotation. The exceptions are listed with a V for their numbers in the fifth edition. A star * indicates that the exercise is considered more challenging. Please try to do as many exercises as possible before the days indicated for them!


Days Exercises
Jan 21 3.1-3.8, 3.13, 3.24, 4.1, 4.2, 5.1-5.12, 5.17, 6.1-6.3, 6.5, 6.9.
Jan 27 and Jan 28 7.1, 7.2, 7.13, 7.14, 7.22*-7.24*, 9.5-9.8 , 10.1-10.3 , 10.13 , 10.25, 10.26, 11.3, 11.13-11.17*, 12.7 , 12.20 , 12.21. 13.5, 13.6, 13.7, 13.9
Feb 3 and Feb 4 13.19*, 13.20, 13.21, 14.3-14.7, 14.9, 14.18, 14.25, 14.14, 14.23, 14.24, 14.31, 14.32, 14.33, 14.34, 15.24*, 16.2, 16.5, 16.7, 16.15, 17.2, 17.4, 17.7, 17.10, 17.12, 17.24, 17.25, 17.27, 17.30, 17.32.
Feb 10 and Feb 11 15.7, 15.9, 15.12, 15.17-15.19, 15.21, 17.14, 17.15*, 18.11*-18.14, 19.1, 19.2-19.5, 19.7, 19.14, 19.15, 19.21=V19.19, 19.22=V19.20, 19.23=V19.21, 19.27=V19.25, 19.32=V19.30, 19.34=V19.32, 21.5-21.10, 21.15-21.18, 21.26-21.28*, 21.34, 21.35.
Feb 17 and Feb 18 22.1, 22.2, 22.6, 22.12, 22.14, determine the quotient groups: (a) 4Z/12Z (b) R # /R >0 , 23.2, 23.4, 23,12, 23.12, 23.13, V23.20*, 56.5= V53.5, 56.6= V53.6, 56.8= V53.8, 56.9= V53.9, 57.5= V54.5, 57.13= V54.13, 58.1= V55.1, 58.2=V55.2, 58.7= V55.7.
Feb 24 and Feb 25 25.1, 25.4, 25.5, 25.7, 25.21, 26.1-26.9, 26.13, 26.18, 26.23*, 27.20*, 27.21, 27.23, 34.6, 34.8, 35.4-35.6, 35.9, 35.12, 35.13, 35.18, 36.1, 36.9, 36.11, 36.12, 36.22*-36.24*, 37.2-37.5, 37.8.
March 3 and March 4

38.1-38.4, 38.9, 38.12-38.15, 38.18*-38.20*, 38.22, 38.24*, show that any R-ideal I which contains an invertertible element is equal to R, 39.1-39.4, 39.7, 39.8*-39.10*, 39.12*, 41.2,41.3, 41.12, 42.4, show that any field of characteristic 0 contains a subfield isomorphic to Q, determine the minimal polynomials for √2+√3 and i=√-1 over Q, 40.6-40.10, 50.3=V45.3, 50.4=V45.4, 50.5=V45.5.

March 10 and March 11 43.1= V44.1, 43.18= V44.18, 30.3, 30.8, 35.14. Let a≠0 and f(x) be a polynomial such that f(xn) is divisible by (x-a). Show that f(xn) is also even divisible by (xn -an).

Solutions to some exercises: Solution to the exercise on Cube.docx


Solutions to the Home Exam (March 21st)

Solutions Algebra home exam March 2020.pdf

Information about the Algebra exam 2020.docx

For examples of previous exams, click here. MMG500 Mar 2017.pdf, MMG500 Jun 2017.pdf

MMG500 Aug 2017.pdf, MMG500 Mar 2018.pdf, MMG500 Jun 2018.pdf

MMG500 Aug 2018.pdf, MMG500 Mar 2019.pdf,  Exam MMG500 Jun 2019.pdf,

Exam MMG500 Aug 2019.pdf

For solutions of exams in 2019, click here. 

Solutions MMG500 Mar 2019.pdf,  Solutions MMG500 June 2019.pdf, 

Solutions MMG500 Aug 2019 corrected.pdf (New Version!)


The dates, times and places for the exams are in the student portal (Links to an external site.).

Examination procedures

In Chalmers Student Portal (Links to an external site.) you can read about when exams are given and what rules apply to exams at Chalmers. In addition to that, there is a schedule (Links to an external site.) when exams are given for courses at the University of Gothenburg. Before the exam, it is important that you sign up for the examination. You sign up through Ladok (Links to an external site.).  At the exam, you should be able to show valid identification. After the exam has been graded, you can see your results in Ladok.

At the annual (regular) examination: 

When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office (Links to an external site.). Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination: 
Exams are reviewed and retrieved at the Mathematical Sciences Student office (Links to an external site.). Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Course evaluation

At the beginning of the course, at least two student representatives should have been appointed to carry out the course evaluation together with the teachers. The evaluation takes place through conversations between teachers and student representatives during the course and at a meeting after the end of the course when the survey result is discussed and a report is written. Guidelines for Course evaluation (Links to an external site.) in Chalmers student portal.

Student representatives

The following students have been appointed:

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Course summary:

Date Details Due