极大序模生成元
Generators of maximal orders
摘要：
设R是数域K中的代数整数环，L是半单K-代数B中的一个极大序模.在我们以前工作的基础上，我们计算了L作为R-代数的最小代数生成元数。这证明并大大扩展了P.A.B.的结果。Pleasants，他考虑了B是数域的情况。为了达到这一目的，我们得到了几个关于具有n个元素的代数的生成元计数的结果。这些结果应该是独立的利益。
英文摘要：
Let R be the ring of algebraic integers in a number field K and let L be a maximal order in a semisimple K-algebra B. Building on our previous work, we compute the smallest number of algebra generators of L considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.
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。
