Group rings that are UJ rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436501" target="_blank" >RIV/00216208:11320/21:10436501 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_W4i490Yac" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_W4i490Yac</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2020.1871000" target="_blank" >10.1080/00927872.2020.1871000</a>

Result language
angličtina
Original language name
Group rings that are UJ rings
Original language description
The set Delta(R) of all elements r of a ring R such that 1 + ru is a unit for every unit u extends the Jacobson radical J(R). R is a UJ ring (Delta U ring, respectively) if its units are of the form 1 +J(R) (1 + Delta(R), respectively). Using a local characterization of Delta U rings, we describe structure of group rings that are UJ rings; if RG is a UJ group ring, then R is a UJ ring, G is a 2-group and, for every nontrivial finitely generated subgroup H of G, the commutator subgroup of H is proper subgroup of H. Conversely, if R is a W ring and G a locally finite 2-group, then RG is a UJ ring. In particular, if G is solvable, RG is a UJ ring if and only if R is UJ and G is a 2-group.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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