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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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.
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