Let be an increasing sequence of ideals in a ring R

1.) Prove that is an ideal.

2.) Prove that if every ideals of R is finitely generated, then exist a number such that

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- Nov 29th 2009, 03:57 AMMagics6rings and ideals
Let be an increasing sequence of ideals in a ring R

1.) Prove that is an ideal.

2.) Prove that if every ideals of R is finitely generated, then exist a number such that

- Nov 29th 2009, 05:13 AMtonio
- Nov 29th 2009, 06:08 AMMagics6
- Nov 29th 2009, 06:52 PMaliceinwonderland
Let ; let and . Without loss of generality, and . Let N=max{m,n}.

Since is an ideal in R, we see that , and . Thus I is an ideal in R.

Quote:

2.) Prove that if every ideals of R is finitely generated, then exist a number such that