Trivial Units for Group Rings with G-adapted Coefficient Rings
| Autor: | M. M. Parmenter, Allen Herman, Yuanlin Li |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Discrete mathematics
Principal ideal ring Pure mathematics Noncommutative ring General Mathematics Polynomial ring 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Category of rings Primitive ring Von Neumann regular ring Zero ring 0101 mathematics Mathematics Group ring |
| Zdroj: | Canadian Mathematical Bulletin. 48:80-89 |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/cmb-2005-007-1 |
| Popis: | For each finite group G for which the integral group ring ℤG has only trivial units, we give ring-theoretic conditions for a commutative ring R under which the group ring RG has nontrivial units. Several examples of rings satisfying the conditions and rings not satisfying the conditions are given. In addition, we extend a well-known result for fields by showing that if R is a ring of finite characteristic and RG has only trivial units, then G has order at most 3. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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