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|
|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  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 . 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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