标题： 物理量作为部分可加域 显示英文标题

标题： Physical quantities as a partially additive field

摘要： 我们通过允许加法成为部分运算来推广域的概念。 我们表明这种“部分加法域”的元素与物理量有许多相似之处。 特别是，它们形成相互可相加元素的子集（类似于物理维度），无量纲元素（那些可与1相加的元素）构成一个域，并且每个元素都可以唯一地表示为一个无量纲元素与同一维度的任何非零元素（单位）的乘积。 我们还讨论了协调单位系统存在的条件。 与之前的工作不同，我们的公理化在一个代数结构中涵盖了量、值、单位和维度，说明部分运算可能为物理世界提供更优雅的描述。 显示英文摘要

摘要： We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually summable elements (similar to physical dimensions), dimensionless elements (those summable with 1) form a field, and every element can be uniquely represented as a product of a dimensionless element and any non-zero element of the same dimension (a unit). We also discuss the conditions for the existence of a coherent unit system. In contrast to previous works, our axiomatization encompasses quantities, values, units, and dimensions in a single algebraic structure, illustrating that partial operations may provide a more elegant description of the physical world.