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Realization problem for von Neumann regular rings
Thesis title in Czech: Realizační problém von Neumannovsky regulárních okruhů
Thesis title in English: Realization problem for von Neumann regular rings
Key words: von Neumannovsky regulární okruh, zjemňující monoid,
English key words: von Neumann regular ring, refinement monoid,
Academic year of topic announcement: 2015/2016
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: 25.09.2015
Date of assignment: 25.09.2015
Confirmed by Study dept. on: 05.10.2015
For a unital ring R, V(R) denotes the monoid of isomorphism of isomorphism classes of finitely generated projective monoids. By a result of Bergman and Dicks [9] every conical monoid with an order unit appears as V(R) of some unital hereditary ring. If a ring R is von Neumann regular, the monoid V(R) is a refinement monoid. F. Wehrung constructed a conical refinement monoid with an order unit of size aleph 2 not isomorphic to V(R) for a von Neumann regular ring [11]. Whether every refinement monoid with an order unit of a smaller size can be represented as V(R) of a regular ring remains, despite of many partial results [2,3,4], open. This problem should be the main task of the thesis.
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