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Linkage of sets of cyclic algebras. (English) Zbl 1478.16011

In this paper, the author studies the existence of a class of cyclic algebras that have no maximal subfield in common. More precisely, let \(F\) be the function field in two algebraically independent variables over a subfield \(F_0\). It is proved that if \(\mathrm{Char } F_0=p\geq 3\) then there exist exactly \(p^2-1\) cyclic algebras of degree \(p\) over \(F\) which share no common maximal subfield. Additionally, the author proves that if \(\mathrm{Char } F_0=0\), then there exist \(p^2\) cyclic algebras of degree \(p\) over \(F\) that have no maximal subfield in common.

MSC:

16K20 Finite-dimensional division rings
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
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