...Equation.3 .Comutativitatea EMBED Equation.3 , EMBED Equation.3 CiXsIntr-adevar, daca EMBED Equation.3 si EMBED Equation.3 , avem EMBED Equation.3 , EMBED Equation.3 Cum adunarea numerelor complexe este comutativa, avem EMBED Equation.3 pentru orice EMBED Equation.3 . Deci EMBED Equation.3 .Element neutru Polinomul constant 00,0,0, este element neutru pentru adunarea polinoamelor, in sensul ca oricare ar fi EMBED Equation.3 CiXs,avem EMBED Equation.3 Elemente inversabileOrice polinom are un opus, adica oricare ar fi EMBED Equation.3 CiXs, exista un polinom, notat EMBED Equation.3 , astfel incat EMBED Equation.3 De exemplu, daca EMBED Equation.3 este un polinom, atunci opusul sau este EMBED Equation.3 EMBED Equation.3 Inmultirea polinoamelorFie EMBED Equation.3 , EMBED Equation.3 Atunci definim EMBED Equation.3 ck EMBED Equation.3 Proprietatile inmultiriiAsociativitateaOricare ar fi EMBED Equation.3 CiXs, avem EMBED Equation.3 ComutativitateaOricare ar fi EMBED Equation.3 CiXs,avem EMBED Equation.3 Intr-adevar, daca EMBED Equation.3 , EMBED Equation.3 , atunci notand EMBED Equation.3 si EMBED Equation.3 , avem EMBED Equation.3 si EMBED Equation.3 . Cum adunarea si inmultirea numerelor complexe sunt comutative si asociative, avem crdr, pentru orice EMBED Equation.3 . Deci EMBED Equation.3 .Element neutruPolinomul 11,0,0, este element neutru pentru inmultirea polinoamelor, adica oricare ar fi EMBED Equation.3 CiXs,avem EMBED Equation.3 Elemente inversabile EMBED Equation.3 CiXs este inversabil daca exista EMBED Equation.3 ,a.i. EMBED Equation.3 Singurele polinoame inversabile sunt cele constante nenule EMBED Equation.3 , a0.DistributivitateaOricare ar fi polinoamele EMBED Equation.3 CiXs,are loc relatia EMBED Equation.3 HaBDFHLNtvxzàaiJ xcM5BCJtphfaj5CJEHUtajtbB5CJOJQJU
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