# Answer to Question #16361 in Abstract Algebra for Melvin Henriksen

Question #16361

Does every simple ring have IBN?

Expert's answer

The answer is "no." Take any nonzero ring R which does not have IBN. Let I be a maximal ideal of R.

Then S = R/ I is a simple ring, and we have a surjection R->S . Since R does not have IBN, it follows that S also does not have IBN.

Then S = R/ I is a simple ring, and we have a surjection R->S . Since R does not have IBN, it follows that S also does not have IBN.

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