Extending abelian groups to rings
نویسندگان
چکیده
منابع مشابه
Extending Abelian Groups to Rings
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 equivalen...
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Let R be a noetherian ring, and G(R) the Grothendieck group of finitely generated modules over R. For a finite abelian group n, we describe G(Rn) as the direct sum of groups G(R’). Each R’ is the form RI<,,, I/n], where n is a positive integer and Cn a primitive nth root of unity. As an application, we describe the structure of the Grothendieck group of pairs (H. u), where His an abelian group ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2007
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700036132