TA: Edwina Aylward

Because of the current situation, all the lectures will be prerecorded and available online on this page, see below.

Sergey Mozgovoy's page for this module contains additional references, as well as lecture notes.

- Chapter 1: Rings

Notes (Complete)

Videos: - Chapter 2: Arithmetic in domains

Notes (Complete, updated to include a proof of Hilbert's basis theorem)

Videos:- The field of fractions of a domain
- Euclidean domains
- Principal ideal domains
- Divisibility, associates, and irreducibles
- Unique factorisation domains: introduction
- Notherian rings, existence of factorisations
- Prime ideals, maximal ideals
- Unique factorisation domains: theorems
- gcd and lcm in a unique factorisation domain
- Factorisation of polynomials 1/3: over a field
- Factorisation of polynomials 2/3: UFD[x] is a UFD
- Factorisation of polynomials 3/3: practical results

- Chapter 3: Field extensions

Notes (Complete)

Videos: - Chapter 4: Modules over a ring

Notes (Complete)

Videos:

Typesetting your work in LaTeX will increase your mark by 20% (but it will still be capped at 100/100).

The solutions will be made available immediately after the deadline, so

Exercise sheet | Due date | Solutions | LaTex source |
---|---|---|---|

Sheet 1 | Friday February 19th, 4PM | Solutions 1 | Source 1 |

Sheet 2 | Friday March 5th, 4PM | Solutions 2 | Source 2 |

Sheet 3 | Monday March 22nd, 4PM | Solutions 3 | Source 3 |

Sheet 4 | Tuesday April 6th, 4PM | Solutions 4 | Source 4 |

Sheet 5 | Monday April 19th, 4PM | Solutions 5 | Source 5 |

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