各种半环中的双运算多集
Bioperational Multisets in Various Semi-rings
摘要：
人们可以找到和与积相等的整数的列表。我们称这样的生物为双操作多重集。似乎没有人在整数以外的领域，如有理数、高斯整数或半环，认真研究过它们。我们列举了所有可能的和产品的双运算多集在整数和六个额外的领域。
英文摘要：
One can find lists of whole numbers having equal sum and product. We call such a creature a bioperational multiset. No one seems to have seriously studied them in areas outside whole numbers such as the rationals, Gaussian integers, or semi-rings. We enumerate all possible sum-products for a bioperational multiset over whole numbers and six additional domains.
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。
