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Give one reason why each of the following rings are not isomorphic..pdf

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Give one reason why each of the following rings are not isomorphic. (Note: Z/81Z is the integers mod 81. Same goes for integers mod 3) Give one reason why each of the following rings are not isomorphic. (a) M2 (Z/3Z) . (Note: Z/81Z is the integers mod 81. Same goes for integers mod 3) Z/81 Z and Z [root 2] X Z [root 2] . (b) Z [root 2] and Solution One way to prove is select a prime number,say p=2,then localize these two rings, one can count the number of elements in both rings and they are NOT equal..

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Give one reason why each of the following rings are not isomorphic. (Note: Z/81Z is the integers mod 81. Same goes for integers mod 3) Give one reason why each of the following rings are not isomorphic. (a) M2 (Z/3Z) . (Note: Z/81Z is the integers mod 81. Same goes for integers mod 3) Z/81 Z and Z [root 2] X Z [root 2] . (b) Z [root 2] and Solution One way to prove is select a prime number,say p=2,then localize these two rings, one can count the number of elements in both rings and they are NOT equal.

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Give one reason why each of the following rings are not isomorphic..pdf

  • 1. Give one reason why each of the following rings are not isomorphic. (Note: Z/81Z is the integers mod 81. Same goes for integers mod 3) Give one reason why each of the following rings are not isomorphic. (a) M2 (Z/3Z) . (Note: Z/81Z is the integers mod 81. Same goes for integers mod 3) Z/81 Z and Z [root 2] X Z [root 2] . (b) Z [root 2] and Solution One way to prove is select a prime number,say p=2,then localize these two rings, one can count the number of elements in both rings and they are NOT equal.