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Local Rings with Elementary Abelian Units

Published online by Cambridge University Press:  20 November 2018

W. K. Nicholson  and
H. J. Springer
W. K. Nicholson
Affiliation:
Department of Math. & Stats., The University of Calgary, Calgary, Alberta, Canada T2N 1N4
H. J. Springer
Affiliation:
Department of Math. & Stats., The University of Calgary, Calgary, Alberta, Canada T2N 1N4
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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 ZkG/E(ZkG) where G is some elementary 2-group and E(ZkG) is the ideal of ZkG generated by {1 - u2:u∈(ZkG)*}.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 205 - 208
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Nicholson, W. K., Local group rings, Can. Math. Bull., 15 (1972), 137–138.CrossRefGoogle Scholar
2. Nicholson, W. K., Semiperfect rings with abelian group of units, Pacific Journal Math. 49 (1973), 191–198.CrossRefGoogle Scholar