Extending abelian groups to rings

• Autores: Lynn M. Batten, Robert S. Coulter, Marie Henderson
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 82, Nº 3, 2007, págs. 297-313
• Idioma: inglés
• DOI: 10.1017/s1446788700036132
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• Resumen

  • 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.