Observations on Primitive, Normal, and Subnormal Elements of Field Extensions
نویسنده
چکیده
Let B1 and B2 be disjoint separable algebraic extensions of a field F, and let B = B1B2 be their composite. Let α1 be an element of B1 and α2 be an element of B2. Suppose α1 and α2 are primitive (resp. normal, resp. subnormal). We investigate the question of when α1 +α2 and α1α2 are necessarily primitive (resp. normal, resp. subnormal) elements of B. (A normal element of a Galois extension is defined to be one that is part of a normal basis, and a subnormal element is defined analogously for a non-Galois extension.)
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