Tsen rank (original) (raw)
In mathematics, the Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. The concept is named for C. C. Tsen, who introduced their study in 1936. We consider a system of m polynomial equations in n variables over a field F. Assume that the equations all have constant term zero, so that (0, 0, ... ,0) is a common solution. We say that F is a Ti-field if every such system, of degrees d1, ..., dm has a common non-zero solution whenever
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| dbo:abstract | In mathematics, the Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. The concept is named for C. C. Tsen, who introduced their study in 1936. We consider a system of m polynomial equations in n variables over a field F. Assume that the equations all have constant term zero, so that (0, 0, ... ,0) is a common solution. We say that F is a Ti-field if every such system, of degrees d1, ..., dm has a common non-zero solution whenever The Tsen rank of F is the smallest i such that F is a Ti-field. We say that the Tsen rank of F is infinite if it is not a Ti-field for any i (for example, if it is formally real). (en) |
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| rdfs:comment | In mathematics, the Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. The concept is named for C. C. Tsen, who introduced their study in 1936. We consider a system of m polynomial equations in n variables over a field F. Assume that the equations all have constant term zero, so that (0, 0, ... ,0) is a common solution. We say that F is a Ti-field if every such system, of degrees d1, ..., dm has a common non-zero solution whenever (en) |
| rdfs:label | Tsen rank (en) |
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