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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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