Prove/Justify. help plz. Remark 8.46. The following facts are easily verified. (a) (A) is the intersection of all ideals containing A. (b) If R is commutative, then (a)-aR :-|ar l r є R. Example 8.47...
Remark 8.46. The following facts are easily verified. (a) (A) is the intersection of all ideals containing A. (b) If R is commutative, then (a)-aR :-|ar l r є R. Example 8.47. In Z, nZ = (n) = (-n). In fact, these are the only ideals in Z (since these are the only subgroups). So, all the ideals in Z are principal. If m and n are positive integers, then nZ C mZ if and only if m divides n. Moreover, we have (m, n) - (d), where d is the greatest common divisor of m andn
Remark 8.46. The following facts are easily verified. (a) (A) is the intersection of all ideals containing A. (b) If R is commutative, then (a)-aR :-|ar l r є R. Example 8.47. In Z, nZ = (n) = (-n). In fact, these are the only ideals in Z (since these are the only subgroups). So, all the ideals in Z are principal. If m and n are positive integers, then nZ C mZ if and only if m divides n. Moreover, we have (m, n) - (d), where d is the greatest common divisor of m andn