batten-extendingabeliangroups-2007.pdf (139.15 kB)
Extending abelian groups to rings
journal contribution
posted on 2007-06-01, 00:00 authored by Lynn BattenLynn Batten, R Coulter, M HendersonFor 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 societyVolume
82Issue
3Pagination
297 - 313Publisher
Cambridge University PressLocation
Melbourne, Vic.ISSN
1446-7887Language
engPublication classification
C1 Refereed article in a scholarly journalCopyright notice
2007, Cambridge University PressUsage metrics
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