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The definition should include sumsets that are not groups. For example, the collection of convex subsets is an Abelian semigroup with identify and with cancellation. There are semigroups without identity in harmonic analysis & probability. Thanks. -- Kiefer.Wolfowitz (talk) 16:49, 11 July 2009 (UTC)[reply]

I changed the redirection page for oplus to redirect to the page Direct_sum_of_modules instead of this one, since it seems a more logical place for the page to redirect to. Ovangle (talk) 5:35, 3 November 2009 (UTC)