Description
Let 𝑀 be the 𝑍-module given by 𝑀=𝑍4𝑁, where 𝑁 is the submodule of 𝑍4 generated by
{(15,1,8,1),(0,2,0,2),(7,1,4,1)}.
(i) Write 𝑀 as a direct sum of non-trivial cyclic 𝑍-modules.
(ii) What is the torsion-free rank of 𝑀 ?
Solved: Let 𝑀 be the 𝑍 – module given by 𝑀 = 𝑍 4 𝑁 , where 𝑁 is the submodule of 𝑍 4 generated by { ( 1 5 , 1 , 8 , 1 ) , ( 0 , 2 , 0 , 2 ) , ( 7 , 1 , 4 , 1 ) } .
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