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For [tex]R_{1}, R_{2}, ..., R_{n}[/tex]

[tex]R_{1} \oplus R_{2} \oplus, ..., R_{n}=(a_{1},a_{2},...,a_{n})|a_{i} \in R_{i}[/tex]

does this mean that a ring which is a direct sum of other rings is composed of specific elements of the original rings that satisfy distribution properties? That is, the first element of the new ring, a1, is from R1 etc for a2 to a_n. Is this correct?