Extending abelian groups to rings
2007 ◽
Vol 82
(3)
◽
pp. 297-314
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Keyword(s):
AbstractFor 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.
1993 ◽
Vol 55
(2)
◽
pp. 238-245
1985 ◽
Vol 32
(1)
◽
pp. 83-92
1979 ◽
Vol 28
(3)
◽
pp. 335-345
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1971 ◽
Vol 12
(2)
◽
pp. 187-192
2015 ◽
Vol 14
(07)
◽
pp. 1550099
◽
2007 ◽
Vol 50
(1)
◽
pp. 37-47
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