Trivial Units for Group Rings with G-adapted Coefficient Rings
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 80-89
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For each finite group $G$ for which the integral group ring $\mathbb{Z}G$ 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.
Herman, Allen; Li, Yuanlin; Parmenter, M. M. Trivial Units for Group Rings with G-adapted Coefficient Rings. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 80-89. doi: 10.4153/CMB-2005-007-1
@article{10_4153_CMB_2005_007_1,
author = {Herman, Allen and Li, Yuanlin and Parmenter, M. M.},
title = {Trivial {Units} for {Group} {Rings} with {G-adapted} {Coefficient} {Rings}},
journal = {Canadian mathematical bulletin},
pages = {80--89},
year = {2005},
volume = {48},
number = {1},
doi = {10.4153/CMB-2005-007-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-007-1/}
}
TY - JOUR AU - Herman, Allen AU - Li, Yuanlin AU - Parmenter, M. M. TI - Trivial Units for Group Rings with G-adapted Coefficient Rings JO - Canadian mathematical bulletin PY - 2005 SP - 80 EP - 89 VL - 48 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-007-1/ DO - 10.4153/CMB-2005-007-1 ID - 10_4153_CMB_2005_007_1 ER -
%0 Journal Article %A Herman, Allen %A Li, Yuanlin %A Parmenter, M. M. %T Trivial Units for Group Rings with G-adapted Coefficient Rings %J Canadian mathematical bulletin %D 2005 %P 80-89 %V 48 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-007-1/ %R 10.4153/CMB-2005-007-1 %F 10_4153_CMB_2005_007_1
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