# Homework for 418H

0.2 : 3,7
0.3 : 3, 4, 7, 9

## Main Course

1.1 : 1abd, 7, 8 13, 14, 22, 25, 35.
1.2 : 1, 4, 7, 18
1.3 : 4, 5, 10, 13, 15, 19
1.4 : 3, 11
1.6 : 3, 4, 6, 9, 18, 25, 26
1.7 : 5, 6.
2.1 : 4, 6, 7, 10, 15
2.2 : 7, 11, 14
2.3 : 2, 3, 9, 11, 13, 16, 19, 25
3.1 : 3, 5, 12, 16, 22, 33, 36, 37, 39
3.2 : 4, 5, 9, 10, 13, 14, 16, 18
3.3 : 3, 4, 7
3.4 : 5, 8, 9, 11
3.5 : 3, 4, 6, 10, 12
4.1 : 1, 4, 8(a), 10
4.2 : 4, 8, 10, 14
4.3 : 5, 6, 8, 13, 19, 22, 30, 35
4.4 : 3, 5, 6, 12, 18
4.5 : 14, 16, 23, 25, 29(Use Prop 23), 32, 36, 39.
7.1 : 3, 7, 11, 14, 26, 27.
7.2 : 3, 5, 12
7.3 : 1, 4, 5, 7, 16, 17, 20, 23, 24, 33
7.4 : 7, 8, 9, 10, 11, 15, 16, 25
7.5 : 3, 4, 5.
Supplemental Exercises
1) Let R be a commutative ring with identity and S a mupltiplicative set such every element of S is a unit in R. Show that ring of fractions of R by S is isomorphic to R.
2) Let R=Z/6Z and S={1,2,4}. Show that S is a multiplicative set. Compute the ring of fractions of R by S. How many elements does it have?

7.6 : 1, 4, 7
8.1 : 2(c), 3, 4(a), 11
8.2 : 1, 4, 5, 6, 8
8.3 : 1, 2, 8(a)
9.1 : 3, 4, 6, 13
9.2 : 1, 3, 5
9.3 : 2, 3