Is a direct sum of two commutative rings still commutative? suppose f is in F,...

zakinutuzi

zakinutuzi

Answered question

2022-01-04

Is a direct sum of two commutative rings still commutative? suppose f is in F, g is in G. why fg=gf?

Answer & Explanation

Beverly Smith

Beverly Smith

Beginner2022-01-05Added 42 answers

Yes. Since multiplication is defined term-wise, commutativity of F⊕G follows from the commutativity of each component.
soanooooo40

soanooooo40

Beginner2022-01-06Added 35 answers

For the reason written above, f,g∈F⊕G, which is commutative. Hence, fg=gf

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