A regular ring whose k₀is not a riesz group^∗

On a density condition for K+0of von neumann regular rings

“…The last result can fail if the ring has pseudo-rank functions that are not rank functions, because the condition (D) can fail. An example of this situation is given by the ring T defined in [8] with constant n = 2: K 0 (T ) is a strictly unperforated group with torsion, but it is not an interpolation group, and it is easy to see that P(T ) = {N }, where KerN = 0 and T /KerN is a commutative field, whence T has a nontrivial artinian homomorphic image and condition (D) fails.…”

Tame and wild refinement monoids

“…As noted in [4, Section 3], the regular rings constructed by Bergman in [19,Example 5.10] and by Menal and Moncasi in [27, Example 2] realize the monoid M constructed in Section 4, so that M could be considered as the most elementary example of a wild refinement monoid. Moncasi constructed in [28] an example of a regular ring R such that K 0 (R) is not a Riesz group. Hence, K 0 (R) + is not a Riesz monoid.…”

Tensor products of structures with interpolation

“…1 (a), it is a refinement monoid whose Grothendieck group is not an interpolation group. Such a situation has already been encountered in [10]: if R is a regular ring, then K 0 (R) is the Grothendieck group of the monoid V(R) of all isomorphism types of finitely generated projective right i?-modules; although V(R) is always a refinement monoid, [10] shows an example where its Grothendieck group is not an interpolation group.…”