Semester 2 test

Question 1

What is a ring?

Answer 1

A set R with binary operation +, ., s.t.

1. (R, +) is abelian.
2. a(bc) = (ab)c Associative
3. (a+b)c = ac + bc
4. Identity element

Question 2

What is a field?

Answer 2

A non=commutative ring with inverses.

Question 3

What is a subring?

Answer 3

A subset of a ring that is a ring under the same binary operation.

Question 4

Define homomorphism

Answer 4

f: R -> S;
1. f(a+b) = f(a) + f(b)
2. f(ab) = f(a)f(b)
3. f(1R) = 1S