Geodesic
On the nonexcellence of field extensions $F(\pi)/F$
Documenta mathematica, Tome 1 (1996), pp. 127-136
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For any n≥3, we construct a field F and an n-fold Pfister form φ such that the field extension F(φ)/F is not excellent. We prove that F(φ)/F is universally excellent if and only if φ is a Pfister neighbor of dimension ≤4.
DOI : 10.4171/dm/6
Classification : 11E04, 11E81, 12F20
Mots-clés : quadratic forms, Pfister forms, excellent field extensions 
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     author = {O.T. Izhboldin},
     title = {On the nonexcellence of field extensions $F(\pi)/F$},
     journal = {Documenta mathematica},
     pages = {127--136},
     year = {1996},
     volume = {1},
     doi = {10.4171/dm/6},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/6/}
}
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O.T. Izhboldin. On the nonexcellence of field extensions $F(\pi)/F$. Documenta mathematica, Tome 1 (1996), pp. 127-136. doi: 10.4171/dm/6

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