(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

α ⊙ (β ⊙ (x, y)) = α ⊙ (β x, β y) = (α(β x), α (β y))
= ((αβ) x, (αβ) y) = (αβ) ⊙ (x, y)
¢ ¡ ¢
1 ⊙ (x, y) = (1x, 1y) = (x, y)
¢ ¢ IR 2 , ⊕, ⊙ ¡
¡ 2 ¨
V = {(x, x ) | x ∈
¢ IR}
V ¢ ¤
IR ×
V V
(x, x2 ) ⊕ (y, y2 ) = 2
x + y, (x + y)
α ⊙ (x, x2 ) = αx, (αx) 2
α x y ∈ IR
(V, ⊕, ⊙)
¡
(x, x 2 ) ⊕ (y, y 2 ) = (x + y, (x + y) 2 ) = (y + x, (y + x) 2 )
¨¥ ¨
(V,
¡ ¢
⊕) © ⊕ (x, x2 2 ) (y, y ) V ∈
= (y, y 2 ) ⊕ (x, x 2 )
¢ ¡
⊕
© ⊕ (x, x 2 2 (y, ) 2 y (z, z ) ∈ 2 IR )
(x, x 2 ) ⊕ ((y, y 2 ) ⊕ (z, z 2 )) = (x, x 2 ) ⊕ (y + z, (y + z) 2 )
= x + (y + z) , (x + (y + z)) 2
((x, x2 ) ⊕ (y, y2 )) ⊕ (z, z2 ) = (x + y, (x + y) 2 ) ⊕ (z, z2 )
= (x + y) + z, ((x + y) + z) 2
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