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Finite Fields ``sets of elements with
addition"
Finite fields are of the form
addition is a usual operation, except multiples of p should be
left out of the set (modulo p). This type of field should not be
confused with finite fields
because
also has
multiplication as an operation. Vectors over
are denoted
, where
is the number of elements in the vector. The
sum of any two vectors in
would be mod p.
Ex: Adding Vectors Over
has 4 elements in each vector
has 6 elements
The additive identity is true for
, so
. For every
element
there is another element
where
.
Ex: Additive Identity
3mod(5) + (-3)mod(5)
3 + 2
0
1mod(5) + (-3)mod(5)
1 + 4
0
2mod(5) + (-3)mod(5)
2 + 2
0
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Frederick Leitner
2004-05-12