I8. Let (R, 1.) be a commutative ring with identity and let N denote the set of nilpotent elements of R. Verify that a) the triple (N,+,) is an ideal of (R,+,). [lint: If a* - - 0, consider (a –...

I8. Let (R, 1.) be a commutative ring with identity and let N denote the set of<br>nilpotent elements of R. Verify that<br>a) the triple (N,+,) is an ideal of (R,+,). [lint: If a* - - 0, consider<br>(a – b)*+

Extracted text: I8. Let (R, 1.) be a commutative ring with identity and let N denote the set of nilpotent elements of R. Verify that a) the triple (N,+,) is an ideal of (R,+,). [lint: If a* - - 0, consider (a – b)*+".) b) the quotient ring (R/N, +, ) has no nonzero nilpotent elements.

Jun 03, 2022

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I8. Let (R, 1.) be a commutative ring with identity and let N denote the set of nilpotent elements of R. Verify that a) the triple (N,+,) is an ideal of (R,+,). [lint: If a* - - 0, consider (a –...

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