Now, we can impose relations among symbols in "X" by taking a quotient. Explicitly, if "E" is a subset of "F", then the quotient ring of "F" by the ideal generated by "E" is called the ring with generators "X" and relations "E". If we used a ring, say, "A" as a base ring instead of Z, then the resulting ring will be over "A". For example, if formula_206, then the resulting ring will be the usual polynomial ring with coefficients in "A" in variables that are elements of "X" (It is also the same thing as the symmetric algebra over "A" with symbols "X".)