Search results
Appearance
There is a page named "Principal fractional ideal" on Wikipedia
- denominators in I {\displaystyle I} , hence the name fractional ideal. The principal fractional ideals are those R {\displaystyle R} -submodules of K {\displaystyle...10 KB (1,605 words) - 19:27, 23 August 2024
- 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...14 KB (2,148 words) - 23:16, 3 August 2024
- I^{*}} . A principal fractional ideal is one of the form x R {\displaystyle xR} for some nonzero x in K. Note that each principal fractional ideal is invertible...24 KB (3,745 words) - 16:27, 10 June 2024
- Algebraic number theory (section Ideal class group)only two ideal classes, the class of principal fractional ideals, and the class of a non-principal fractional ideal such as (2, 1 + √-5). The ideal class...40 KB (5,798 words) - 13:01, 5 July 2024
- an ideal in order theory is derived from the notion of ideal in ring theory. A fractional ideal is a generalization of an ideal, and the usual ideals are...37 KB (6,303 words) - 12:06, 9 August 2024
- integers R. Let S be a finite set of prime ideals of R. An element x of K is an S-unit if the principal fractional ideal (x) is a product of primes in S (to...5 KB (528 words) - 03:39, 27 February 2023
- Takagi existence theorem (redirect from Generalized ideal class group)ideals do not involve any prime ideal appearing in mf). The smaller one, Pm, is the group of principal fractional ideals (u/v) where u and v are nonzero...6 KB (828 words) - 16:32, 14 July 2024
- fractional ideals form a group under a product. The quotient of the group of fractional ideals by the subgroup of principal ideals is then the ideal class...7 KB (1,095 words) - 22:00, 9 May 2024
- Hecke character (section Definition using ideals)denote the group of fractional ideals of K relatively prime to mf and let Pm denote the subgroup of principal fractional ideals (a) where a is near 1...13 KB (1,738 words) - 16:35, 15 August 2024
- every nonzero fractional ideal of R is irreducible in the sense that it cannot be written as a finite intersection of fractional ideals properly containing...11 KB (1,526 words) - 16:38, 5 July 2024
- Glossary of commutative algebra (redirect from Saturated ideal)of non-zero fractional ideals, where two such ideals are called equivalent if they are contained in the same principal fractional ideals. 2. A Weil divisor...66 KB (9,767 words) - 00:23, 7 July 2024
- {\displaystyle {\mathcal {I}}_{B}} be the ideal groups of A and B, respectively (i.e., the sets of nonzero fractional ideals.) Following the technique developed...6 KB (1,079 words) - 05:10, 6 January 2023
- condition (ACC) and descending chain condition (DCC) Fractional ideal Ideal class group Radical of an ideal Hilbert's Nullstellensatz Flat module Flat map Flat...4 KB (301 words) - 17:28, 20 December 2023
- Divisor (algebraic geometry) (redirect from Principal Weil divisor)group generated by all divisors) is closely related to the group of fractional ideals for a Dedekind domain. An algebraic cycle is a higher codimension...40 KB (6,609 words) - 18:59, 14 April 2023
- where IK is the group of fractional ideals of K, and PK is the subgroup of principal fractional ideals of K, that is, ideals of the form aOK where a is...5 KB (809 words) - 23:32, 20 August 2023
- Commutative ring (section Principal ideal domains){\displaystyle s} . Such an ideal is called a principal ideal. If every ideal is a principal ideal, R {\displaystyle R} is called a principal ideal ring; two important...41 KB (5,655 words) - 15:25, 12 December 2023
- Ring (mathematics) (section Ideal)are left ideals and right ideals, respectively; they are called the principal left ideals and right ideals generated by x. The principal ideal RxR is written...99 KB (13,632 words) - 08:46, 14 August 2024
- cover general valuation rings and Krull rings. To this day, Krull's principal ideal theorem is widely considered the single most important foundational...17 KB (2,020 words) - 15:41, 6 May 2024
- ideal b {\displaystyle \mathbf {b} } such that the product ideal a b {\displaystyle \mathbf {ab} } is a principal ideal." Two (integral or fractional)...18 KB (4,127 words) - 02:31, 23 January 2024
- received a special name, such as normal subgroup for groups and two-sided ideals for rings. Kernels allow defining quotient objects (also called quotient...18 KB (2,553 words) - 09:07, 5 May 2024
- 1911 Encyclopædia Britannica/Number (redirect from 1911 Encyclopædia Britannica/Number/Fractional Numbers){o}}} ) form an ideal; this is called a principal ideal, and is denoted by o α {\displaystyle {\mathfrak {o}}\alpha } . Every ideal can be represented
- designated by writing the denominator and then placing over it a dot. Fractional values which could not be expressed by any one unit-fraction were expressed
- viscous losses to the wall inside the cylindrical bore, while only a fractional part of energy is radiated via bell and open holes and heard by listeners