Where \ mathcal { O } is the ring of integers in a finite extension of \ mathbb { Q } _ \ ell.
22.
Gauss sums over a residue ring of integers mod " N " are linear combinations of closely related sums called Gaussian periods.
23.
The congruence classes with these two defined operations form a ring, called the "'ring of integers modulo " '.
24.
More generally, if is the spectrum of the ring of integers of an algebraic number field, then is the Dedekind zeta function.
25.
Rings that also satisfy commutativity for multiplication ( such as the ring of integers ) are called "'commutative rings " '.
26.
The ring of integers ( that is, the set of integers with the natural operations of addition and multiplication ) satisfy many important properties.
27.
Choosing the ideal \ langle 2 \ rangle in the ring of integers, the corresponding principal congruence subgroup defines this surface of genus 7.
28.
Developed a more general framework to define the intersection pairing defined on an arithmetic surface over the spectrum of a ring of integers by Arakelov.
29.
In algebraic number theory, " R " will be taken to be the ring of integers, which is Dedekind and thus regular.
30.
Namely, in the ring of integers of the appropriate number field, the rational prime 13 splits as a product of three distinct prime ideals.
