A theorem named for this mathematician states that a prime ideal of a field is ramified in a finite separable extension of that field if and only if it divides the discriminant of the field extension.
Raising a function named for this mathematician to the twenty-fourth power, then multiplying by two pi to the twelfth  power,  is  equivalent to  cubing  the  g-sub-two  invariant  of  a  Weierstrass  elliptic  function,  then subtracting twenty-seven times the g-sub-three invariant. A theorem named for this mathematician states that a prime ideal of a field is ramified in a finite separable extension of that field if and only if it divides the discriminant of the field extension. Multiplying an integer n by the product over all its prime factors p of "one plus one over p" gives this mathematician's namesake (*) psi function. Every nonzero prime ideal is maximal in this mathematician's namesake type of integrally closed Noetherian domain. He names an operation that partitions a totally ordered set into a closed upwards set and a closed downwards set that has no greatest element. For 10 points, the rational numbers can be used to construct the real numbers via what mathematician's namesake "cuts"? 
Raising a function named for this mathematician to the twenty-fourth power, then multiplying by two pi to the twelfth  power,  is  equivalent to  cubing  the  g-sub-two  invariant  of  a  Weierstrass  elliptic  function,  then subtracting twenty-seven times the g-sub-three invariant.
Julius Wilhelm Richard  Dedekind