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Extending abelian groups to rings

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journal contribution
posted on 2007-06-01, 00:00 authored by Lynn BattenLynn Batten, R Coulter, M Henderson
For any abelian group G and any function f : G → G we define a commutative binary operation or `multiplication' on G in terms of f. We give necessary and sufficient conditions on f for G to extend to a commutative ring with the new multiplication. In the case where G is an elementary abelian p-group of odd order, we classify those functions which extend G to a ring and show, under an equivalence relation we call weak isomorphism, that there are precisely six distinct classes of rings constructed using this method with additive group the elementary abelian p-group of odd order p2.

History

Journal

Journal of the Australian mathematical society

Volume

82

Pagination

297 - 313

Location

Melbourne, Vic.

Open access

  • Yes

ISSN

1446-7887

Language

eng

Publication classification

C1 Refereed article in a scholarly journal

Copyright notice

2007, Cambridge University Press

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