1.
Let R be a ring such that x^2=x for all x belong R.
Show that R is commutative.
2.
Let R be a commutative ring. If Mis an ideal, abbreviate MM by M^2.
Let M_1, M_2 be two ideals such that M_1+M_2=R.
Show that M_1 ^2 + M_2 ^2 =R
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Logic is invincible because in order to combat logic
it is necessary to use logic.
（邏輯是不可戰勝的，因為要反對邏輯還得使用邏輯。）
By Pierre Boutroux
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