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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
Thesis language: angličtina
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
Guidelines
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.

References
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[4] K. R. Goodearl, “Von Neumann Regular Rings”. Pitman, London, 1979. xvii + 369 pp.
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and Monographs)”. AMS, 1986; xxii + 336 pp.
[6] K. R. Goodearl, Von Neumann regular rings and direct sum decomposition problems. Abelian
Groups and Modules, Kluwer, Dordrecht, 1995, 249–255.
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[8] F. Wehrung, Non measurability properties of interpolation vector spaces. Israel Journal of
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[9] F. Wehrung, Coordinatization of lattices by regular rings without unit and Banaschewski
functions. Algebra Universalis 64 (2010), no. 1-2, 49–67.
 
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