# Answer to Question #24893 in Abstract Algebra for Hym@n B@ss

Question #24893

For any ideal A in a ring R, show that √A consists of s ∈ R such that every n-system containing s meets A.

Expert's answer

*√*A is defined to be the set of

*s*

*∈*

*R*such that every

*m*-system containing

*s*meets A. The desired conclusion, therefore, follows from the following twofacts: (1) every

*m*-system is an

*n*-system,and

(2) if

*N*is an

*n*-systemand

*s*

*∈*

*N*, then there exists an

*m*-system

*M*such that

*s*

*∈*

*M*

*⊆*

*N .*

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