j****l
发帖数: 4 | 1 IF S is a ring with the property that s=s^2 for each s belongs to S, which of
the following must be true?
1. s+s=0 for each s belongs to S
2. (s+t)^2=s^2+t^2 for each s, t belong to S
3. S is commutative
I'm engineering student. I tried to read abstract algebra textbook, but it's
difficult..... Could anyone solve it for me with a little bit more detailes?
Thanks in advance for your help. | B****n
发帖数: 11290 | 2 (s+s)^2=s+s=>s+s=0...1
(s+t)^2=s+t=s^2+t^2
(s+t)^2=s^2+t^2+st+ts=s+t+st+ts=>st+ts=0
by 1=>st=ts
of
【在 j****l 的大作中提到】
: IF S is a ring with the property that s=s^2 for each s belongs to S, which of
: the following must be true?
: 1. s+s=0 for each s belongs to S
: 2. (s+t)^2=s^2+t^2 for each s, t belong to S
: 3. S is commutative
: I'm engineering student. I tried to read abstract algebra textbook, but it's
: difficult..... Could anyone solve it for me with a little bit more detailes?
: Thanks in advance for your help.
| x*****d
发帖数: 427 | 3 How did you get 1?
【在 B****n 的大作中提到】
: (s+s)^2=s+s=>s+s=0...1
: (s+t)^2=s+t=s^2+t^2
: (s+t)^2=s^2+t^2+st+ts=s+t+st+ts=>st+ts=0
: by 1=>st=ts
:
: of
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