Assume a ring $R$ is isomorphic to direct product of $F_1,F_2,F_3$
We can denote this by
$R\cong F_1\times F_2 \times F_3$
Is this equivalent to
$R\cong F_1\oplus F_2 \oplus F_3$ ???
How to denote isomorphism/ ring direct product
1
$\begingroup$
direct-product
module-isomorphism
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2Use $\times$ in that first line instead of $\otimes$ (which is something else, namely a tensor product) – 2017-02-16
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1As Mark said, don't use $\otimes$, use $\times$. As far as the content of your question, the direct product and direct sum amount to the same thing when you have finitely many terms. – 2017-02-16
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0Thanks all, I should have use $\times$ instead of $\otimes$ – 2017-02-16