Let $R(G)$ be a given abelian group ring. Any abelian group ring is isomorphic to an abelian ring. I know how to express (isomorphism) some group rings as a ring. But I wonder if there is a general method for finding how to write a given abelian group ring as an abelian ring ? I mean a method that is not trial and error. Also it must be efficient and always halt to the correct answer.
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