Non-stable K theory of regular rings
| Název práce v češtině: | |
|---|---|
| Název v anglickém jazyce: | Non-stable K theory of regular rings |
| Klíčová slova anglicky: | K -theory, von Neuman regular ring, refinement monoid, countable, |
| Akademický rok vypsání: | 2011/2012 |
| Typ práce: | disertační práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra algebry (32-KA) |
| Vedoucí / školitel: | doc. Mgr. Pavel Růžička, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 26.09.2012 |
| Datum zadání: | 26.09.2012 |
| Datum potvrzení stud. oddělením: | 08.11.2012 |
| Zásady pro vypracování |
| 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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| Seznam odborné literatury |
| [1] P. Ara, The realization problem for von Neumann regular rings. “RING THEORY 2007
Proceedings of the Fifth China–Japan–Korea Conference Tokyo, Japan, 10 – 15 September 2007”, 2008, 316 pp. [2] P. Ara, The regular algebra of a poset. Trans. Amer. Math. Soc. 362 (2010), no. 3, 1505-1546. [3] P. Ara, M. Brustenga, The regular algebra of a quiver. J. Algebra, 309 (2007), 207-535. [4] K. R. Goodearl, “Von Neumann Regular Rings”. Pitman, London, 1979. xvii + 369 pp. [5] K. R. Goodearl, “Partially Ordered Abelian Groups with Interpolation (Mathematical Surveys 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. [7] J. Moncasi, A regular ring whose K0 is not a Riesz group. Comm. Algebra 13 (1985), no. 1, 125-131. [8] F. Wehrung, Non measurability properties of interpolation vector spaces. Israel Journal of Mathematics 103, no. 1 (1998), 177–206. [9] F. Wehrung, Coordinatization of lattices by regular rings without unit and Banaschewski functions. Algebra Universalis 64 (2010), no. 1-2, 49–67. |