威尔逊定理
Wilson's theorem
摘要：
证明了数域上整数环的商的乘法群中所有元素的乘积有四种可能性，并给出了每种可能性出现的精确条件.威尔逊定理的这种推广原来是由M. Laššák（2000），但我们的证明更简单、更直接。
英文摘要：
We show that there are four possibilities for the product of all elements in the multiplicative group of a quotient of the ring of integers in a number field, and give precise conditions for each of the possibilities to occur. This generalisation of Wilson's theorem turns out to have been first discovered by M. Laššák (2000), but our proof is simpler and more direct.
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。
