## S.V.Duzhin

### Algebra

#### Lectures at the University of Pereslavl, Autumn 2000

**Time and place:** Thursdays 9:45--11:20, Main building
of UP.

Materials available so far (in Russian, unless otherwise specified):

- Course program

- September 7. Lecture 1. Transformation groups:
TeX file,
PostScript,
JPEG: page 1,
page 2.

- September 14. Lecture 2. General notion of a group:
TeX file,
PostScript,
JPEG: page 1.
page 2,
page 3.

- September 21. Lecture 3. The Lagrange theorem:
TeX file,
PostScript,
JPEG: page 1.
page 2.

- September 28. Lecture 4. Generators. Isomorphism:
TeX file.

- October 5. Lecture 5. Permutations. Cayley theorem.

- October 12. Test on group theory.
Variant 1,
Variant 2.

- October 19. Discussion of test problems.

- October 26. Lecture 6. Homomorphism and quotient groups.
(Notes about homomorphisms (in English):
Page 1,
Page 2,
Page 3).

- November 2. Lecture 7. Rings and fields (in English).
JPEG: Page 1,
Page 2,

PostScript: full text,

- November 9. Lecture 8. Subring, ideal, quotient ring.
JPEG,
PostScript
(in English).

- November 16. Lecture 9. Finite fields.

- November 23. Lecture 10. Finite-dimensional algebras
over the real numbes.

S.V.Duzhin