A $K\_0$-avoiding dimension group with an order-unit of index two
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2005-05-20 | |
| dc.date | 2005-06-01 | |
| dc.date.accessioned | 2026-07-07T06:33:06Z | |
| dc.date.available | 2026-07-07T06:33:06Z | |
| dc.description | 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. | |
| dc.description | To appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0505426 | |
| dc.identifier | http://arxiv.org/abs/math/0505426 | |
| dc.identifier | Journal of Algebra 301, no. 2 (2006) 728--747 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99085 | |
| dc.subject | General Mathematics | |
| dc.subject | 06B10, 06C05, 16E50, 19A49 | |
| dc.title | A $K\_0$-avoiding dimension group with an order-unit of index two | |
| dc.type | text |