I have to find the projective dimension of Z/pZ as Z-module, Z/pZ-module and Z/(p^2)Z-module, p is prime.Could anyone help me?
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Originally Posted by Veve I have to find the projective dimension of Z/pZ as Z-module, Z/pZ-module and Z/(p^2)Z-module, p is prime.Could anyone help me? let clearly as module is free and so projective. thus as module is torsion and so it's not projective. now consider the exact sequence as modules: hence is projective. thus finally looking at as module we have this exact sequence: but as module: therefore:
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