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Partition Rings of Cyclic Groups of Odd Prime Power Order1

Published online by Cambridge University Press:  20 November 2018

K. I. Appel
K. I. Appel*
Affiliation:
University of Michigan and Institute for Defence Analyses, Princeton
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A ring R over a commutative ring K, that has a basis of elements g1, g2, … , gn forming a group G under multiplication, is called a group ring of G over K. Since all group rings of a given G over a given K are isomorphic, we may speak of the group ring KG of G over X.

Let π be any partition of G into non-empty sets GA, GB, … . Any subring P of KG that has a basis of elements

is a partition ring of G over K.

If P is a partition ring of G over Z, the ring of integers, then the basis A, B, … for P clearly serves as a basis for a partition ring P’ = Q ⊗ P of G over Q, the field of rationals.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 373 - 391
Copyright
Copyright © Canadian Mathematical Society 1961

References

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