Lie rings are also useful in the definition of a p-adic analytic groups and their endomorphisms by studying Lie algebras over rings of integers such as the p-adic integers.
42.
*PM : unique factorization and ideals in ring of integers, id = 9171 new !-- WP guess : unique factorization and ideals in ring of integers-- Status:
43.
*PM : unique factorization and ideals in ring of integers, id = 9171 new !-- WP guess : unique factorization and ideals in ring of integers-- Status:
44.
*PM : examples of ring of integers of a number field, id = 6879-- WP guess : examples of ring of integers of a number field-- Status:
45.
*PM : examples of ring of integers of a number field, id = 6879-- WP guess : examples of ring of integers of a number field-- Status:
46.
In particular, Kodaira gave a " p "-adic integers ) and Dedekind domains ( e . g ., the ring of integers of a number field ).
47.
It follows that Pic ( " R " ) is a finite group ( finiteness of class number ) that measures the deviation of the ring of integers from being a PID.
48.
This section constructs the ring of integers, the fields of rational and real numbers, and " vector-families ", which are related to what are now called torsors over abelian groups.
49.
Lichtenbaum conjectured that special values of the zeta function of a number field could be expressed in terms of the " K "-groups of the ring of integers of the field.
50.
Computation of the class group is hard, in general; it can be done by hand for the ring of integers in an algebraic number field of small discriminant, using Minkowski's bound.
