Unformatted text preview: r 2 R and m 2 M . Then the homomorphism property of ' translates into mixed associative and distributive laws: .r 1 r 2 /m D r 1 .r 2 m/ and .r 1 C r 2 /m D r 1 m C r 2 m: Moreover, '.r/ 2 End .M/ translates into the second distributive law: r.m 1 C m 2 / D rm 1 C rm 2 : Conversely, given a product R ² M ±! M satisfying the mixed associative law and the two distributive laws, for each r 2 R , deﬁne the map '.r/ W M ! M by '.r/.m/ D rm . Then the second distributive law says 345...
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 Fall '08
 EVERAGE
 Algebra, Addition, Algebraic structure, mixed associative law

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