Local Group Rings
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 137-138
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The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan which characterized local group rings when both the ring and the group are commutative.We assume throughout that all rings are associative with identity. If R is a ring we call R local if R/J(R) is a division ring where J(R) denotes the Jacobson radical of R. It is well known that R is local if and only if each element of R\J(R) is a unit. We need the following.
Nicholson, W. K. Local Group Rings. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 137-138. doi: 10.4153/CMB-1972-025-1
@article{10_4153_CMB_1972_025_1,
author = {Nicholson, W. K.},
title = {Local {Group} {Rings}},
journal = {Canadian mathematical bulletin},
pages = {137--138},
year = {1972},
volume = {15},
number = {1},
doi = {10.4153/CMB-1972-025-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-025-1/}
}
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