论文标题
指数向量空间的基础和维度
Basis and Dimension of Exponential Vector Space
论文作者
论文摘要
指数向量空间[jutimly \ emph {evs}]是矢量空间的代数阶序列，因为每个evs都包含一个向量空间，相反，每个矢量空间都可以嵌入到这样的结构中。该EVS结构由半群结构，标量乘法和部分顺序组成。在本文中，我们通过借助部分秩序和代数操作引入有序独立集合和生成集合的思想来开发电动汽车的基础和维度概念。我们发现，像向量空间一样，电动汽车不始终包含基础。我们已经为电动汽车建立了必要和充分的条件。结果表明，维度的平等性是EVS属性，但相反的是不正确的。我们已经研究了Subevs的维度，发现每个EV都包含一个具有所有可能较低维度的Subevs。最后，我们已经计算出某些电动汽车的基础和维度，这些电动汽车通过在不同方面创建反示例来帮助我们探索基础理论。
Exponential vector space [shortly \emph{evs}] is an algebraic order extension of vector space in the sense that every evs contains a vector space and conversely every vector space can be embedded into such a structure. This evs structure consists of a semigroup structure, a scalar multiplication and a partial order. In this paper we have developed the concepts of basis and dimension of an evs by introducing the ideas of orderly independent set and generating set with the help of partial order and algebraic operations. We have found that like vector space, an evs does not contain basis always. We have established a necessary and sufficient condition for an evs to have a basis. It was shown that equality of dimension is an evs property but the converse is not true. We have studied the dimension of subevs and found that every evs contains a subevs with all possible lower dimensions. Lastly we have computed basis and dimension of some evs which help us to explore the theory of basis by creating counter examples in different aspects.
