1+1 este inversabil intr-un inel cu un nr. impar de elem.?
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bogdanl_yex
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1+1 este inversabil intr-un inel cu un nr. impar de elem.?
Fie \( A \) un inel unitar cu un numar impar de elemente. \( 1+1 \) este inversabil in acest caz?
"Don't worry about your difficulties in mathematics; I can assure you that mine are still greater"(Albert Einstein)
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bogdanl_yex
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Grupul aditiv \( (A,+) \) are
\( ord(A)=2k+1 \Rightarrow \underbrace{1+1+...+1}_{2k+1}=0 \).
Deci
\( \underbrace{1+1+...+1}_{2k}=-1\Rightarrow (1+1) \underbrace{(1+1+...+1)}_{k}=-1 \Rightarrow 1+1 \)
este inversabil.
\( ord(A)=2k+1 \Rightarrow \underbrace{1+1+...+1}_{2k+1}=0 \).
Deci
\( \underbrace{1+1+...+1}_{2k}=-1\Rightarrow (1+1) \underbrace{(1+1+...+1)}_{k}=-1 \Rightarrow 1+1 \)
este inversabil.
"Don't worry about your difficulties in mathematics; I can assure you that mine are still greater"(Albert Einstein)