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

Question

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

Answer 1

√A is defined to be the set of s ∈ R such that every m-system containing smeets 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-systemM such that s ∈ M ⊆ N .