Suggested Problems

Here is a list of suggested problems from textbook of the lecture.

(Elements of Modern Algebra by Jimmy Gilbert, Linda Gilbert )

Section Suggested Problems
1.4 1,2,3,4,5,6
1.6 1,2,3,4
3.1 15,  16, 17, 18, 19, 20, 30, 31, 32.
3.2 4, 9, 10, 13,  14, 15.
3.3 (Subgroups) 2, 3, 4, 6, 8, 14, 15, 17, 19, 20
3.4 (Cyclic Groups) 6, 7, 8, 9, 14, 15,  16, 18, 21, 22, 25, 26, 28, 31, 32, 36.
3.5 (Isomorphisms) 1, 2, 6, 7, 15, 18, 20, 34
3.6 (Homomorphisms) 1, 4, 5, 6, 8, 9, 19, 20
4.1 (Finite  Permutation Groups) 1(all), 2(all), 3, 4, 5, 6, 7, 8,
9, 10, 11
4.4(Cosets  of  a  Subgroup) 1, 2, 3, 4, 16, 18, 21
4.5(Normal Subgroups) 1, 2, 4, 6, 8, 9, 10, 16, 17, 18, 19, 20, 22
4.6(Quotient Groups) 1, 2, 3, 5, 6, 7, 8, 10, 11, 21, 22
5.1(Definition of  a Ring) 1, 2, 3, 4, 7, 19, 21, 27, 28, 29, 36, 37, 38
5.2(Intergral Domains  and  Fields) 1, 2, 3, 4, 5, 8(replace the word “assume” with “prove” !) 9, 10, 11, 12, 20.
6.1(Ideals  and  Quotient Rings) 4, 6, 9, 10, 11, 16, 21, 24
6.2(Ring  Homomorphisms) 6, 8, 9, 13, 14, 15
7.2 (Complex Numbers and  Quaternions) 1 – 12, 19, 20, 21
8.1(Polynomials over a Ring) 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 17, 18
8.2(Divisibility and Greatest Common Divisor) 1 – 6, 7 – 10, 11 – 14,
15, 16, 17, 1, 23, 25, 29, 34
8.3(Factorization in F[x]) 1(all), 2(all), 3, 4(all), 9, 12(a, b), 13
8.4(Zeros  of  a  Polynomial)  1(all), 2(all), 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 20, 21