(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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76 CAPÍTULO 7. £¡ §© ¢¦£ ¤ ¢¥ § ¡<br />
¡ § ⊕ +<br />
<br />
IR<br />
2 (x, x ) ∈ IR 2 <br />
2<br />
x, x ⊕ e, e 2 = x, x 2<br />
⊕ ©<br />
¢¡ <br />
<br />
2<br />
x + e, (x + e) = x, x 2 ⇐⇒<br />
(e, e 2 ) ∈ IR 2 <br />
<br />
x + e = x<br />
(x + e) 2 = x 2 =⇒ e = 0<br />
(0, 0) ¡ K ⊕<br />
<br />
<br />
©<br />
⊕ (x, x 2 ) ∈ IR 2 <br />
(y, y2 ) ∈ IR 2 <br />
x, x 2 ⊕ y, y 2 = (0, 0)<br />
¢¡ <br />
<br />
2<br />
x + y, (x + y) = (0, 0) ⇐⇒<br />
x + y = 0<br />
(x + y) 2 = 0<br />
=⇒ y = −x<br />
2 (−x, x )<br />
¡ (x, x 2 ¢ ⊕<br />
) <br />
¨§ <br />
<br />
(x, x 2 ), (y, y2 ) ∈ IR 2 <br />
(K, ⊕) ¡ ¢ (K, ⊕, ⊙) ¡ <br />
<br />
α IR ∈<br />
α ⊙ ((x, x2 ) ⊕ (y, y2 )) = α ⊙ (x + y, (x + y) 2 )<br />
= α(x + y), (α(x + y)) 2<br />
<br />
(α ⊙ (x, x2 )) ⊕ (α ⊙ (y, y2 )) = α x, (α x) 2 ⊕ α y, (α y) 2<br />
<br />
= α x + α y, (α x + α y) 2<br />
α ⊙ x, x 2 ⊕ y, y 2 = α ⊙ x, x 2 ⊕ α ⊙ y, y 2