Exercises:Rings and Modules - 2016 - 1/Problem 2

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Problems

Problem 2

Part A

Compute the homology groups at Q5 and Z5 of the the following complexes:

  1. with f1:=(011011210011010) and f2:=(1101122022)
  2. with f1:=(011011210011010) and f2:=(1101122022)
Solution

Part B

Let:

be a commutative diagram of R-modules in which the rows are exact sequences. Show the Five lemma:

  • If f1,f2,f4 and f5 are isomorphism then so is f3
Solution

Notes

References