# Answer to Question #25247 in Abstract Algebra for Mohammad

Question #25247

Show that from Kothe’s Conjecture (“The sum of two nil left ideals in any ring is nil”.) followsthe statement:

if I is a nil ideal in any ring R, then Mn(I) is nil for any n.

if I is a nil ideal in any ring R, then Mn(I) is nil for any n.

Expert's answer

Note that Mn(I) equals sum of all J

_{k}where J_{k}is the left ideal in Mn(R) consisting of matrices with k-thcolumn entries from I and all other entries zero. Then, each J_{k}isnil, so by assumption (and induction), M_{n}(I) is nil.Need a fast expert's response?

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