Non-stable K theory of regular rings
|Thesis title in Czech:|
|Thesis title in English:||Non-stable K theory of regular rings|
|English key words:||K -theory, von Neuman regular ring, refinement monoid, countable,|
|Academic year of topic announcement:||2011/2012|
|Type of assignment:||dissertation|
|Department:||Department of Algebra (32-KA)|
|Supervisor:||doc. Mgr. Pavel Růžička, Ph.D.|
|Author:||hidden - assigned and confirmed by the Study Dept.|
|Date of registration:||26.09.2012|
|Date of assignment:||26.09.2012|
|Confirmed by Study dept. on:||08.11.2012|
|Let R be a ring. The monoid of projective modules, V(R), is the set of isomorphism classes of finitely generated projective left R-modules with the opeartion corresponding to the direct sum of the modules. For a von Neumann regular ring R, V(R) is a refinement conical monoid. In general, the problem of the realization of a refinement monoid as the monoid V(R) for a regular ring R has a negative answer due to F. Wehrung. However the problem remains open for countable refinement monoids. This is connected to the seperativity problem, in particular, to the question whether every von Neumann regular ring is separative. A positive answer to the above realization problem would reject the separativity conjecture.
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