m n n 5. (2+3=5 points) Suppose R is a ring such that Z CRCQ. (a) Prove that if me R with m and n relatively prime integers, then the R. (b) Prove that R is a PID. Tip: Let I be an ideal of R and consider A ZnI. In this case, it will be helpful to write aR and aZ for the principal ideals of R and Z respectively, as the notation (a) will be ambigu

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m n n 5. (2+3=5 points) Suppose R is a ring such that Z CRCQ. (a) Prove that if me R with m and n relatively prime integers, then the R. (b) Prove that R is a PID. Tip: Let I be an ideal of R and consider A ZnI. In this case, it will be helpful to write aR and aZ for the principal ideals of R and Z respectively, as the notation (a) will be ambiguous.

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