[代數] unity和inverse的唯一性

[mqazz1 (無法顯示)]

proof

(1) if R has a unity, it is unique

        我這樣證: let u1, u2 be two unity

        u1 = u1 * u2 = u2

        u1 = u2, so unity is unique

        請問這樣證有問題嗎?

(2) if R has a unity and x is a unit of R, the multiplicative inverse of x

    is unique

請問這題應該怎麼證呢?


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推 znmkhxrw    :(1)you are right (2)suppose y,z are inverse of x
→ znmkhxrw    :xy=e=xz , so xy=xz , apply "y" y(xy)=y(xz)
→ znmkhxrw    :=(yx)y=(yx)z=ey=ez=y=z