ideal class group
1Ideal class group — In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by a certain group known as an ideal class group (or class group). If… …
2Ideal norm — In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an… …
3Class field theory — In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields. Most of the central results in this area were proved in the period between 1900 and 1950. The theory takes its name… …
4Class number formula — In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function Contents 1 General statement of the class number formula 2 Galois extensions of the rationals 3 A …
5Class number — In mathematics, class number may refer to Class number (group theory), the number of conjugacy classes of a group The size of the ideal class group of a number ring The number of equivalence classes of binary quadratic forms of a given… …
6Ideal theory — In mathematics, ideal theory is the theory of ideals in commutative rings; and is the precursor name for the contemporary subject of commutative algebra. The name grew out of the central considerations, such as the Lasker Noether theorem in… …
7Ideal number — In mathematics an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind s definition of ideals for rings. An ideal in the ring …
8Class-D amplifier — Block diagram of a basic switching or PWM (class D) amplifier A class D amplifier or switching amplifier is an electronic amplifier where all power devices (usually MOSFETs) are operated as binary switches. They are either fully on or fully… …
9Hilbert class field — In algebraic number theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K . Its degree over K equals the class number of K and the Galois group of E over K is canonically isomorphic to the ideal… …
10Fractional ideal — In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral… …
