ONM problema 2

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bogdanl_yex
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ONM problema 2

Post by bogdanl_yex »

Fie \( (A,+,\cdot) \) un inel comutativ finit. Notam cu \( d \) numarul divizorilor lui zero iar cu \( n \) numarul elementelor nilpotente ale inelului. Sa se arate ca:
a) daca \( x \) si \( y \) sunt nilpotente, atunci \( x+y \)si \( xy \) sunt nilpotente.
b)\( n \) divide \( d \).
"Don't worry about your difficulties in mathematics; I can assure you that mine are still greater"(Albert Einstein)
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