6. Fields & Vector Spaces

Question 1

Field

Answer 1

A set F with 2 binary operations, addition and multiplication where they satisfy:

1. F is an abelian group under addition
2. F* is an abelian group under multiplication
3. Distributive law holds a(b+c)=ab+ac

Question 2

Subfield

Answer 2

A subset of F is a subfield if F’ is a field under multiplication and addition

Question 3

Basic number fields

Answer 3

Set of rational numbers, set of complex numbers, set of real numbers

Question 4

Vector Space

Answer 4

Let V be a set on 2 operations, addition and scalar multiplication then V is a vector space if the 6 specified axioms (in notes) are held