域上特征多项式满足的条件与division algebras
Conditions satisfied by characteristic polynomials in fields and division algebras
摘要：
假设E/F是一个域扩张。我们问是否存在一个元素E的特征多项式有一个或多个零系数在指定的位置。我们发现，答案往往是“不”。我们还证明了类似的结果，司代数，并表明，普遍的司代数的次数n不具有一个元素的迹0和范数1。
英文摘要：
Suppose E/F is a field extension. We ask whether or not there exists an element of E whose characteristic polynomial has one or more zero coefficients in specified positions. We show that the answer is frequently ``no''. We also prove similar results for division algebras and show that the universal division algebra of degree n does not have an element of trace 0 and norm 1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
