序单位为2的$K\_0$ -回避维数群
A $K\_0$-avoiding dimension group with an order-unit of index two
摘要：
证明了存在一个维数群$G$，它的正锥不同构于任意格$L$的维数幺半群$L$ .维度组$G$有一个顺序单位，并且可以采用任何大于或等于$\aleph\_2$的基数。对于确定Dim函子范围内维数群的正锥，$\aleph\_2$界是最优的.这否定地解决了作者在1998年提出的问题，即任何锥加细么半群是否同构于某个格的维数么半群。由于$G$具有指数为2的序单元，这也否定地解决了K.R.关于序单位为2的维数群关于$K\_0$的单位正则环的可表示性的Goodearl.
英文摘要：
We prove that there exists a dimension group $G$ whose positive cone is not isomorphic to the dimension monoid Dim$L$ of any lattice $L$. The dimension group $G$ has an order-unit, and can be taken of any cardinality greater than or equal to $\aleph\_2$. As to determining the positive cones of dimension groups in the range of the Dim functor, the $\aleph\_2$ bound is optimal. This solves negatively the problem, raised by the author in 1998, whether any conical refinement monoid is isomorphic to the dimension monoid of some lattice. Since $G$ has an order-unit of index two, this also solves negatively a problem raised in 1994 by K.R. Goodearl about representability, with respect to $K\_0$, of dimension groups with order-unit of index 2 by unit-regular rings.
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