![]() ![]() For every $a\in A$, the factorization of the corresponding divisor $\phi(a)$ into the product of prime ideal numbers can be looked at as a substitute for unique factorization into prime factors if factorization in $A$ is not unique.įor example, the ring $A$ of integers of the field $\mathbf Q(\sqrt)$, where $m\in\mathbf Q(\zeta)$. Ideal numbers were introduced in connection with the absence of uniqueness of factorization into prime factors in the ring of integers of an algebraic number field. They can be identified in a natural way with the ideals (cf. ![]() In modern terminology, ideal numbers are known as integral divisors of $A$. The semi-group $D$ is a free commutative semi-group with identity its free generators are called prime ideal numbers. Divisor) of the ring $A$ of integers of an algebraic number field. An element of the semi-group $D$ of divisors (cf. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |