rayne said:Let F ={0 , 1 , a , b} be a field with four elements. What is a + b^2 and a^2 + b^2.
Apparently, the answers are b and 1, respectively. How do we come to that conclusion?
A field is a mathematical structure that consists of a set of elements along with two operations, addition and multiplication. These operations follow certain rules, such as commutativity and distributivity, and every element in the set has an inverse under both operations.
There are four elements in the field F: 0, 1, a, and b. This is stated in the given information "Let F = {0, 1, a, b} be a field with four elements."
The operations in the field F are addition and multiplication. These operations are defined for each pair of elements in the set and follow certain rules, such as commutativity and distributivity.
The inverse of an element in the field F is the element that, when combined with the original element under either addition or multiplication, results in the identity element. In this case, the identity element for addition is 0 and the identity element for multiplication is 1.
Yes, the field F is a commutative field. This means that the order in which the elements are combined under addition or multiplication does not affect the result. This is stated in the given information "F ={0 , 1 , a , b} be a field with four elements."