12-240/Classnotes for Thursday September 13

From Drorbn
Jump to navigationJump to search

In the second day of the class, the professor continues on the definition of a field.

Definition of a field

Combined with a part from the first class, we have a complete definition as follow:

A field is a set "F' with two binary operations +,x defind on it, and two special elements 0 ≠ 1 such that

F1: commutative law

a, b F: a+b=b+a and a.b=b.a

F2: associative law

a, b, c F: (a+b)+c=a+(b+c) and (a.b).c= a.(b.c)


F3: the existence of identity element

a+o=a and a.1=a