Let be $R$ a ring conmutative whith unity and $G_1,$ $G_2$ multiplicative groups. Prove the $R(G_1\times G_2)\cong (RG_1)G_2$.
I tried prove that $r_{gh}(g,h)\mapsto (r_{gh}g)h$ is an isomorphism , but I can't the lineality of the sum.
2026-04-17 08:22:38.1776414158
About group algebras. Are $R(G_1\times G_2)$, $(RG_1)G_2$ isomorphic?
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