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.
Unless expressly stated otherwise, the copyright for items in Deakin Research Online is owned by the author, with all rights reserved.
Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO.
If you believe that your rights have been infringed by this repository, please contact firstname.lastname@example.org.