# MATH 322 - Modern Algebra

Fall 2018

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  MW 10:20-10:50 am, F 12:25-12:55, WF 2-2:30 pm, M 3-3:30 and by appointment.
Telephone:
(505) 277-2214

email: jvassil@math.unm.edu

webpage: http://www.math.unm.edu/~jvassil

## Binary Operations

1: 22, 31, 33, 36
2: 2, 4, 5, 8, 20, 24, 26, 27, 28, 36

## Isomorphic structures

3: 2, 4, 7, 10, 11, 16, 24, 27, 28
4: 2, 4, 5, 10

## Cyclic subgroups and groups

4: 23, 25, 29, 32, 35, 41
5: 4, 6, 15, 16, 20, 39, 47, 54, 56

## Dihedral Groups and Permutations

6: 6(use euclidean algorithm to express gcd in terms of the given integers), 10, 18, 23, 32, 34, 37, 44, 46, 50

## Permutations and Cayley's Theorem

8: 2, 5, 9, 16, 24, 32, 35, 36, 40, 41
9: 2, 8, 10, 14, 34

## Cosets and Lagrange

10: 4, 12, 15, 19, 20, 24, 30, 32, 33, 39, 40, 44

## Homomorphisms

11:  6, 8, 11, 14, 18, 23, 24, 32, 34, 36
13: 18, 20, 22, 26

## Factor Groups

11: 46, 50
13: 29, 32, 36, 38, 42, 44, 45, 50
14: 5, 6, 10, 14, 21, 22, 23

## Group Actions

14: 31, 35, 36
15: 5, 8, 9, 14, 19, 37
16: (1, 2, 3 please use our notation for D_4 in these problems), 8, 12, 13

## Rings

16: (9,10 use our notation not that of the book), 11
17: 2, 7, 8

## Rings and ring homomorphisms

18: 10, 12, 18, 25, 33, 37, 38, 44, 46, 50, 55
19: 10, 17, 28, 29

## Field of Quotients

20:  4, 5, 6, 10, 12, 14, 18, 23, 27, 29
21: 4, 12, 14, 15

## Factorization of polynomials

22: 3, 5, 9, 13, 21, 23, 25, 27
23: 2, 4, 10

## Factor Rings and Ideals

23: 14, 16, 19, 25, 28, 34, 35

26: 3, 4, 10, 13, 25, 27