Fie \( A \) un inel cu proprietatea ca \( x^6=x \) pentru orice x din A . Aratati ca :
a) \( x^2=x \)
b) A este inel comutativ
Inel cu x^6 =x
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Bogdan Posa
- Pitagora
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- Location: Motru , Gorj , Romania
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Inel cu x^6 =x
Gradul de cultură al unei ţări se măsoară astăzi, prin nivelul matematic al locuitorilor ţării (André Lichnerowicz)
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Beniamin Bogosel
- Co-admin
- Posts: 710
- Joined: Fri Mar 07, 2008 12:01 am
- Location: Timisoara sau Sofronea (Arad)
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Se observa usor ca \( 1+1=0 \) si \( x+1=(x+1)^6=x^6+x^4+x^2+1 \Rightarrow x^4=x^2=x^6=x \) adica \( x^2=x \). Punctul celalalt e destul de cunoscut...
Yesterday is history,
Tomorow is a mistery,
But today is a gift.
That's why it's called present.
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Tomorow is a mistery,
But today is a gift.
That's why it's called present.
Blog