Nonstable K theory of regular rings
Thesis title in Czech:  

Thesis title in English:  Nonstable 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 
Thesis language:  angličtina 
Department:  Department of Algebra (32KA) 
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 
Guidelines 
Let R be a ring. The monoid of projective modules, V(R), is the set of isomorphism classes of finitely generated projective left Rmodules 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.

References 
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