Neoplatonism
Submodules of Z[x,y]
Let M = Z[1/2,1/5] (ring of polynomials evaluated at 1/2 and 1/5 with integer coefficients))
Then let K = Z[1/2] a submodule of M.
Does the following calculation hold for M/K?
Take 9/10 from M, then what is its congruence in M/K?
9/10 = 5/10 + 4/10 = 1/2 + 2/5 and since 1/2 is from K, then
9/10 is congruent to 2/5 + K in M/K?
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