Let p be a prime integer and F the function field in two algebraically independent variables over a smaller field $F_0$. We prove that if $\mathrm{char}(F_0)=p⩾3$ then there exist $p^2-1$ cyclic algebras of degree p over F that have no maximal subfield in common, and 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.

中文翻译：

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循环代数集的链接

设p为素数，F为较小域上两个代数独立变量中的函数域$F_0$. 我们证明如果$\mathrm{字符}(F_0)=磷⩾3$ 那么存在 ${磷}^2-1$在F上没有最大子域的p 次循环代数，如果$\mathrm{字符}(F_0)=0$ 那么存在 ${磷}^2$在F上没有最大子域的p 次循环代数。