Question

If i and j are ideal in r then i+j is also an ideal in r

Answer 1

For ideals, it is the ideal generated by all the products ij, where i∈I,j∈J, in other words, it the set of all finite sums

{i1j1+…injnfor some n∈N,ik∈I,jk∈J}.

Note that if I and J are principal ideals, generated by a and b respectively, IJ is but the principal ideal generated by

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