Answer to Question #23264 in Abstract Algebra for Melvin Henriksen
A is in I or B is in I. Thus image of I will be 0 in R/I and images of A and B
will be some ideals A', B', The inclusion A'B' is in 0 is preserved, and its
conclusion A' is 0 or B' is 0 is preserved too. Thus R /I is prime ring.
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