Search results
Results from the WOW.Com Content Network
Ideal class group. In number theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK /PK where JK is the group of fractional ideals of the ring of integers of K, and PK is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of ...
It follows that composition induces a well-defined operation on primitive classes of discriminant , and as mentioned above, Gauss showed these classes form a finite abelian group. The identity class in the group is the unique class containing all forms x 2 + B x y + C y 2 {\displaystyle x^{2}+Bxy+Cy^{2}} , i.e., with first coefficient 1.
Form (education) A form is an educational stage, class, or grouping of pupils in a school. The term is used predominantly in the United Kingdom, although some schools, mostly private, in other countries also use the title. Pupils are usually grouped in forms according to age and will remain with the same group for a number of years, or ...
This is not a Weyl group and has no connection with the Weil–Châtelet group or the Mordell–Weil group. The Weil group of a class formation with fundamental classes u E/F ∈ H 2 (E/F, A F) is a kind of modified Galois group, introduced by Weil (1951) and used in various formulations of class field theory, and in particular in the Langlands program.
Homeroom. A homeroom, tutor group, form class, or form is a brief administrative period that occurs in a classroom assigned to a student in primary school and in secondary school. Within a homeroom period or classroom, administrative documents are distributed, attendance is marked, announcements are made, and students are given the opportunity ...
The narrow class group features prominently in the theory of representing integers by quadratic forms. An example is the following result (Fröhlich and Taylor, Chapter V, Theorem 1.25). Theorem. Suppose that where d is a square-free integer, and that the narrow class group of K is trivial. Suppose that.
Two divisors are said to be linearly equivalent if their difference is principal, so the divisor class group is the group of divisors modulo linear equivalence. For a variety X of dimension n over a field, the divisor class group is a Chow group; namely, Cl(X) is the Chow group CH n−1 (X) of (n−1)-dimensional cycles. Let Z be a closed ...
The word "class" in the term "equivalence class" may generally be considered as a synonym of "set", although some equivalence classes are not sets but proper classes. For example, "being isomorphic " is an equivalence relation on groups, and the equivalence classes, called isomorphism classes, are not sets. The set of all equivalence classes in ...