Question III: Let M₁ and M₂ be two R-modules and let r E R. Let M₁ X M₂ = {(x,y) |x E M₁, y € M₂} with operations (x₁, y₁) + (x₂,Y₂) = (x₁+x₂, Y₁ + y₂) and r. (x, y) = (r.x, r.y) Show that M₁ X M₂ is an R-module.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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algebra module over ring
Question III:
Let M₁ and M₂ be two R-modules and let r ER. Let M₁ X M₂ =
operations
{(x,y)|x E M₁, y € M₂} with
(X₁,Y₁) + (x₂,Y₂) = (x₁+x₂, Y₁ + y₂) and r. (x, y) = (r.x, r.y)
Show that M₁ X M₂ is an R-module.
Transcribed Image Text:Question III: Let M₁ and M₂ be two R-modules and let r ER. Let M₁ X M₂ = operations {(x,y)|x E M₁, y € M₂} with (X₁,Y₁) + (x₂,Y₂) = (x₁+x₂, Y₁ + y₂) and r. (x, y) = (r.x, r.y) Show that M₁ X M₂ is an R-module.
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