24. Let (R, +,) be a commutative ring with identity and a ER be an idempotent which is different from 0 or 1. Prove that (R, t,) is the direet sum of the principal ideals ((a), +,-) and ((1 - a), +,):...

24. Let (R, +,) be a commutative ring with identity and a ER be an idempotent<br>which is different from 0 or 1. Prove that (R, t,) is the direet sum of the principal<br>ideals ((a), +,-) and ((1 - a), +,): R - (a) e (1 – a). (llint: Utilize the faet<br>a. (I - a) = 0.]<br>%3D<br>

Extracted text: 24. Let (R, +,) be a commutative ring with identity and a ER be an idempotent which is different from 0 or 1. Prove that (R, t,) is the direet sum of the principal ideals ((a), +,-) and ((1 - a), +,): R - (a) e (1 – a). (llint: Utilize the faet a. (I - a) = 0.] %3D

Jun 03, 2022

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24. Let (R, +,) be a commutative ring with identity and a ER be an idempotent which is different from 0 or 1. Prove that (R, t,) is the direet sum of the principal ideals ((a), +,-) and ((1 - a), +,):...

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