zakinutuzi

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?

Beverly Smith

Yes. Since multiplication is defined term-wise, commutativity of $F\oplus G$ follows from the commutativity of each component.

soanooooo40

For the reason written above, $f,g\in F\oplus G$, which is commutative. Hence, $fg=gf$