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Question regarding notation of internal/ external direct sum.

I am referring to Richard Pierce's book Associative Algebras, where he uses two notations for direct sum $\oplus$ and $\dotplus$.

I am assuming one of them refers to external direct sum, one refers to internal direct sum, but not sure which is which?

Thanks for help.

Update: In the beginning of the book the author said "We will denote the product of a finite set $\{A_1,A_2,\dots,A_n\}$ of algebras by $A_1\dotplus A_2\dotplus \dots \dotplus A_n$."

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    $\begingroup$ Does he not state his convention somewhere near the beginning of the book? This is not a standard convention I've ever seen... $\endgroup$ – Eric Wofsey Feb 24 '16 at 7:43
  • $\begingroup$ He said "We will denote the product of a finite set $\{A_1,A_2,\dots,A_n\}$ of algebras by $A_1\dotplus A_2\dotplus \dots \dotplus A_n$. $\endgroup$ – yoyostein Feb 24 '16 at 7:47
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According to the index of symbols at the end of the book, $\dotplus$ denotes the product of algebras, while $\oplus$ denotes the direct sum of modules.

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  • $\begingroup$ By product, does he mean Cartesian Product? $\endgroup$ – yoyostein Feb 24 '16 at 7:49
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    $\begingroup$ Yes (well, he defines it as the categorical product, but that is the same thing, up to canonical isomorphism). $\endgroup$ – Eric Wofsey Feb 24 '16 at 7:50

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