Let R be a commutative ring with unity Let X be a subset of R. Prove...

 

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Let R be a commutative ring with unity Let X be a subset of R. Prove that there exists a smallest ideal in R which contains X. (An ideal is said to be smallest ideal satisfying a given condition c, if for every ideal b satisfying condition c, a C b. That is, a Cb whenever b is an ideal satisfying condition c.) This ideal is denoted by < X >. Let R be a commutative ring with unity Let X be a subset of R. Prove that there exists a smallest ideal in R which contains X. (An ideal is said to be smallest ideal satisfying a given condition c, if for every ideal b satisfying condition c, a C b. That is, a Cb whenever b is an ideal satisfying condition c.) This ideal is denoted by < X >.