Geodesic
Local Rings with Elementary Abelian Units
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 205-208

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In [2] the structure of all semiperfect rings with abelian group of units has been obtained in terms of commutative local rings. It follows easily that the structure of semiperfect rings with elementary abelian group of units is determined by commutative local rings whose unit groups are elementary abelian. In this note such local rings are completely characterized. It is shown that a local ring having an elementary abelian group of units has characteristic two, four or eight and is a homomorphic image of Z k G/E(Z k G) where G is some elementary 2-group and E(Z k G) is the ideal of Z k G generated by {1 - u 2:u∈(Z k G)*}. 
Nicholson, W. K.; Springer, H. J. Local Rings with Elementary Abelian Units. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 205-208. doi: 10.4153/CMB-1976-031-0
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     title = {Local {Rings} with {Elementary} {Abelian} {Units}},
     journal = {Canadian mathematical bulletin},
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     year = {1976},
     volume = {19},
     number = {2},
     doi = {10.4153/CMB-1976-031-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-031-0/}
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