유한체에서의 덧셈을 정의할 때 그 결과가 여전히 유한체에 속해 있도록 해야 합니다. 즉 수학
용어로 유한체에서 덧셈이 닫혀 있도록 해야 합니다.
방금 배운 나머지연산으로 덧셈을 정의하면 유한체에서 덧셈이 닫혀 있도록 할 수 있습니다.
다음과 같이
19
를 위수로하는 유한체가 있다고 합시다.
F
19
=
{0
,
1
,
2
, ...
18}
여기에서
a
,
b
∈
F
19
이고 기호 ∈는 왼쪽의 원소가 오른쪽 집합에 속해 있다는 뜻입니다.
a
,
b
는
F
19
의 원소입니다.
덧셈에 대해 닫혀 있다는 뜻은 다음과 같습니다.
a
+
f
b
∈
F
19
1
장
유한체
45
여기서는 일반 정수에서의 덧셈과 구별하기
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