论文标题
关于线性映射定义中条件的独立性（修订）
On the independence of conditions in the linear mapping definition (revised)
论文作者
论文摘要
我们研究了在同一标量场上对向量空间之间的线性映射定义中添加性和均匀性条件的（在）依赖性。与其他关于该主题的作品不同，处理了真实或复数等特定领域，或者处理连续或可衡量的特定映射，我们考虑了总体情况。这使我们能够获得完整的图片。也就是说，对于主要领域，并且仅在这种情况下，条件是依赖的（添加性意味着同质性）。对于非优势领域，它们是独立的：两个条件都不意味着另一个条件。因此，在此处解决了上一篇文章中提出的问题。
We study the (in)dependence of additivity and homogeneity conditions in the definition of linear mappings between vector spaces over the same scalar field. Unlike other works on the subject, dealing with particular fields like real or complex numbers, or with particular mappings like continuous or measurable, we consider the general case. This enables us to obtain complete picture. Namely, for the prime field, and only in this case, the conditions are dependent (additivity implies homogeneity). For the non-prime field they are independent: neither of conditions implies the other. Thus, the problem posed in the previous version of the paper, is solved here.
