A K0-avoiding dimension group with an order-unit of index two

JOURNAL OF ALGEBRA

卷:301

Article

Wehrung, Friedrich

关键词: lattice;    monoid;    dimension monoid;    dimension group;    index;    V-homomorphism;    modular lattice;    Von Neumann regular ring;    locally matricial;   

DOI  :  10.1016/j.jalgebra.2005.06.003

来源: Elsevier

【 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 N-2. As to determining the positive cones of dimension groups in the range of the Dim functor, the N-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 2, 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. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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