Kommutativer Halbring/Allgemeines Distributivgesetz/Fakt

Allgemeines Distributivgesetz (kommutativer Halbring)

Es sei ${}R$ ein kommutativer Halbring und es seien ${}a_{1},\ldots ,a_{r},b_{1},\ldots ,b_{s}$ Elemente aus ${}R$ .

Dann gilt das allgemeine Distributivgesetz

${}{\left(\sum _{i=1}^{r}a_{i}\right)}{\left(\sum _{k=1}^{s}b_{k}\right)}=\sum _{1\leq i\leq r,\,1\leq k\leq s}a_{i}b_{k}\,.$

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