Field is integral domain and is a such that every non-zero elemen in it has multiplicative inverse. Extension field F of field K is splitting field of collections polinomial { fi(x) | i Î I } of K if F is the smallest subfield containing K and all the zeros in of the polinomial fi(x). Elemen a Î F is algebra over K if f (a) = 0 for some 0 ¹ f (x) Î K[x]. Splitting field is extension algebra.
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Last update: 2025-04-07 02:12:35