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Extending abelian groups to rings

Batten, Lynn, Coulter, Robert S. and Henderson, Marie 2007, Extending abelian groups to rings, Journal of the Australian mathematical society, vol. 82, no. 3, pp. 297-313.

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Title Extending abelian groups to rings
Author(s) Batten, Lynn
Coulter, Robert S.
Henderson, Marie
Journal name Journal of the Australian mathematical society
Volume number 82
Issue number 3
Start page 297
End page 313
Publisher Cambridge University Press
Place of publication Melbourne, Vic.
Publication date 2007-06
ISSN 1446-7887
Summary 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.
Language eng
Field of Research 010101 Algebra and Number Theory
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2007, Cambridge University Press
Persistent URL http://hdl.handle.net/10536/DRO/DU:30007153

Document type: Journal Article
Collections: School of Engineering and Information Technology
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