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L’élimination linéaire dans les corps. (Linear elimination in skew fields). (French) Zbl 0587.03024
We show that for a skew field the following conditions for equivalent: (i) to be finite dimensional over its centre; (ii) to have 2-linear elimination; (iii) to have linear elimination; (iv) to have elimination of inverses.

MSC:
03C60 Model-theoretic algebra
12E15 Skew fields, division rings
16Kxx Division rings and semisimple Artin rings
12L12 Model theory of fields
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