Slide 11
Slide 11 text
ͷఆٛ
ू߹ R ͕(ring)Ͱ͋Δͱɺͱੵͷू߹͕ఆٛ͞Ε͓ͯΓҎԼͷ͕݅Γཱͭ࣌
ʹ͍͏
∀x, y ∈ R, xy ∈ R, x + y ∈ R (ԋࢉʹؔͯ͠ด͍ͯ͡Δ)
∃0R
∈ R, ∀x ∈ R, 0R
+ x = x + 0R
= x (ͷ୯Ґݩͷଘࡏ)
∀x, y ∈ R, x + y = y + x (ͷަ๏ଇ)
∀x, y, z ∈ R, (x + y) + z = x + (y + z) (ͷ݁߹๏ଇ)
∀x ∈ R, ∃ − x ∈ R, x + (−x) = (−x) + x = 0R
(ͷٯݩͷଘࡏ)
∃1R
∈ R, ∀x ∈ R, 1R
x = x1R
= x (ੵͷ୯Ґݩͷଘࡏ)
∀x, y, z ∈ R, (xy)z = x(yz) (ੵͷ݁߹๏ଇ)
∀x, y, z ∈ R, (x + y)z = xz + yz, x(y + z) = xy + xz (๏ଇ)
( Z )ͦͷͱੵͷԋࢉʹؔͯ͠Ͱ͋Δ
՝
R ʹ͍ͭͯɺ ∀x ∈ R, x0R
= 0R
x = 0R
Λࣔͤ(ิ: (−1R
)x = −x Λࣔͤ)
·ͨɺ(−1R
)(−1R
) = 1R
Λࣔͤ
܂ാӳࢿ (@mather314) ฏͷֶษڧձ 2 ճ 2017/10/24 11 / 15