Ring of integer-valued polynomials over rational integers

Symbol-free definition
The ring of integer-valued polynomials over rational integers is defined in the following equivalent ways:


 * It is the ring of integer-valued polynomials over the ring of rational integers.
 * It is the ring generated by binomial polynomials over the ring of rational integers.

Facts

 * Ring of integer-valued polynomials over rational integers is an interpolation domain: An integer-valued polynomial of degree $$n$$ can be interpolated using its values at any $$n + 1$$ consecutive integers; moreover, the values at $$n+1$$ consecutive integers can be any tuple whatsoever.
 * Ring of integer-valued polynomials over rational integers is not Noetherian
 * Ring of integer-valued polynomials over rational integers is not a UFD