In this paper, the composition of Bhargava’s cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields. The exclusion of the latter case arises from the nonexistence of a bijection between (classes of) binary quadratic forms and an ideal class group. This problem, together with a related mistake in another paper of the author, is addressed in the appendix.

中文翻译：

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Bhargava 立方体在数域上的组合

在本文中，巴尔加瓦立方体的组成被推广到窄类第一数域的整数环，排除全虚数域的情况。排除后一种情况是因为二元二次形式（的类）与理想类群之间不存在双射。这个问题以及作者另一篇论文中的相关错误在附录中得到了解决。