$K_0$ groups of noncommutative ${\mathbb{R}}^{2n}$

In this paper we show that the $K_0$ groups of noncommutative ${\mathbb{R}}^{2n}$ are $\mathbb{Z}$ for $\mathrm{\forall }n\in {\mathbb{N}}^{\ast }$ and make an approach to the calculation of the smooth case, which will bring many new sequence problems relating to binomial numbers.