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Longer titles found: Principal ideal domain (view), Principal ideal ring (view), Principal ideal theorem (view), Structure theorem for finitely generated modules over a principal ideal domain (view), Krull's principal ideal theorem (view), Ascending chain condition on principal ideals (view)

searching for Principal ideal 37 found (235 total)

alternate case: principal ideal

Solid set (380 words) [view diff] exact match in snippet view article find links to article

{\displaystyle S.} An ideal generated by a singleton set is called a principal ideal in X . {\displaystyle X.} The intersection of an arbitrary collection

Ramsey cardinal (556 words) [view diff] exact match in snippet view article find links to article

Ramseyness and measurability is existence of a κ-complete normal non-principal ideal I on κ such that for every A ∉ I and for every function f: [κ]<ω →

Ideal (order theory) (1,766 words) [view diff] exact match in snippet view article

given element p is a principal ideal and p is said to be a principal element of the ideal in this situation. The principal ideal ↓ p {\displaystyle \downarrow

Freudenthal spectral theorem (493 words) [view diff] exact match in snippet view article find links to article

property and e any positive element in E. Then for any element f in the principal ideal generated by e, there exist sequences { s n } {\displaystyle \{s_{n}\}}

Eisenstein's criterion (3,592 words) [view diff] exact match in snippet view article find links to article

invertible in F[x]); in this case a possible choice of prime ideal is the principal ideal generated by any irreducible element of D. The latter statement gives

Finite group (1,831 words) [view diff] exact match in snippet view article find links to article

both simplified and generalized to finitely generated modules over a principal ideal domain, forming an important chapter of linear algebra. A group of

List of theorems called fundamental (553 words) [view diff] exact match in snippet view article find links to article

abelian groups Fundamental theorem of finitely generated modules over a principal ideal domain Fundamental theorem of finite distributive lattices Fundamental

Ruth Charney (603 words) [view diff] case mismatch in snippet view article find links to article

Institutions Brandeis University Thesis Homological Stability for the General Linear Group of a Principal Ideal Domain (1977) Doctoral advisor Wu-Chung Hsiang

Completeness (order theory) (1,924 words) [view diff] exact match in snippet view article

obvious embedding e: X → D(X) that maps each element x of X to its principal ideal {y in X | y ≤ x}. A little reflection now shows that e has a lower

Divisible group (1,411 words) [view diff] exact match in snippet view article find links to article

injective modules. Thus in the case of the ring of integers Z, which is a principal ideal domain, a Z-module (which is exactly an abelian group) is divisible

Universal coefficient theorem (1,181 words) [view diff] exact match in snippet view article find links to article

case of the Bockstein spectral sequence. Let G be a module over a principal ideal domain R (e.g., Z or a field.) There is also a universal coefficient

Tangent cone (1,080 words) [view diff] exact match in snippet view article find links to article

= − y . {\displaystyle x=y,\quad x=-y.} Its defining ideal is the principal ideal of k[x] generated by the initial term of f, namely y2 − x2 = 0. The

F-crystal (864 words) [view diff] exact match in snippet view article find links to article

module over the Witt ring. More precisely since the Witt ring is a principal ideal domain, the module M/FM can be written as a direct sum of indecomposable

Hilbert symbol (1,571 words) [view diff] exact match in snippet view article find links to article

elements of the number field by putting (a b)=(a (b)) where (b) is the principal ideal generated by b. Hilbert's reciprocity law then implies the following

Stone duality (2,289 words) [view diff] exact match in snippet view article find links to article

V p −1(0) (since p preserves arbitrary suprema). In addition, the principal ideal p −1(0) is a prime ideal since p preserves finite infima and thus the

Artin reciprocity (2,340 words) [view diff] exact match in snippet view article find links to article

specifically, the conductor of L / Q {\displaystyle L/\mathbb {Q} } is the principal ideal (Δ) or (Δ)∞ according to whether Δ is positive or negative, and the

Power residue symbol (1,321 words) [view diff] exact match in snippet view article find links to article

}{(\beta )}}\right)_{n},} where ( β ) {\displaystyle (\beta )} is the principal ideal generated by β . {\displaystyle \beta .} Analogous to the quadratic

Riesz space (5,296 words) [view diff] exact match in snippet view article find links to article

{\displaystyle A.} An Ideal generated by a singleton is called a principal ideal. A band B {\displaystyle B} in a Riesz space E {\displaystyle E} is

Glossary of order theory (4,210 words) [view diff] exact match in snippet view article find links to article

filter is called principal filter if it has a least element. Dually, a principal ideal is an ideal with a greatest element. The least or greatest elements

Integral closure of an ideal (698 words) [view diff] exact match in snippet view article find links to article

{\overline {xI}}=x{\overline {I}}} . In particular, in a normal ring, a principal ideal generated by a non-zerodivisor is integrally closed. Let R = k [ X

Culture of India (18,634 words) [view diff] exact match in snippet view article find links to article

epic played a pivotal role in establishing the role of dhárma as a principal ideal guiding force for Hindu way of life. The earliest parts of the Mahabharata

Éléments de mathématique (3,074 words) [view diff] case mismatch in snippet view article find links to article

Groups and Fields 7 Modules sur les anneaux principaux 7 Modules over Principal Ideal Domains Algèbre: Chapitre 8 8 Modules et anneaux semi-simples Algebra:

Dedekind–MacNeille completion (2,726 words) [view diff] exact match in snippet view article find links to article

A ⊆ B as sets. An element x of S embeds into the completion as its principal ideal, the set ↓x of elements less than or equal to x. Then (↓x)u is the

Leech lattice (4,304 words) [view diff] exact match in snippet view article find links to article

{Q} ({\sqrt {-23}})} . Multiplying this Niemeier lattice by a non-principal ideal of the ring of integers gives the Leech lattice. Raji (2005) constructed

Inverse semigroup (3,748 words) [view diff] exact match in snippet view article find links to article

F-inverse semigroup if and only if Y {\displaystyle {\mathcal {Y}}} is a principal ideal of X {\displaystyle {\mathcal {X}}} and X {\displaystyle {\mathcal

Pell's equation (6,598 words) [view diff] exact match in snippet view article find links to article

(2007), "Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem", Journal of the ACM, 54 (1): 1–19, doi:10.1145/1206035.1206039

Stable range condition (546 words) [view diff] exact match in snippet view article find links to article

Related Stable Range Conditions, Series in Algebra 11, World Scientific, Hackensack, NJ, 2011. [1] Bass' stable range condition for principal ideal domains

Integral element (5,304 words) [view diff] exact match in snippet view article find links to article

ideal is an operation of schemes which replaces the given ideal with a principal ideal. The normalization of a scheme is simply the scheme corresponding to

Infrastructure (number theory) (2,490 words) [view diff] exact match in snippet view article

MR790655 J. Buchmann, H. C. Williams: On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. Math. Comp. 50

Gauss composition law (4,127 words) [view diff] exact match in snippet view article find links to article

O({\sqrt {d}})} . An ideal a {\displaystyle \mathbf {a} } is called a principal ideal if there exists an algebraic integer α {\displaystyle \alpha } such

Proofs of quadratic reciprocity (4,009 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (x-{\sqrt {p^{*}}},q)} of K. It certainly divides the principal ideal (q). It cannot be equal to (q), since x − p ∗ {\displaystyle x-{\sqrt

Glossary of category theory (10,474 words) [view diff] exact match in snippet view article find links to article

integer exists. For example, the homological dimension of ModR with a principal ideal domain R is at most one. homotopy category See homotopy category. It

Adele ring (18,442 words) [view diff] exact match in snippet view article find links to article

for the maximal ideal of O v . {\displaystyle O_{v}.} If this is a principal ideal denoting the uniformising element by π v . {\displaystyle \pi _{v}

Congruence lattice problem (5,500 words) [view diff] exact match in snippet view article find links to article

(Dobbertin 1986). Every distributive (∨,0)-semilattice in which every principal ideal is at most countable is representable. Problem 2 (Dobbertin 1983).

AN codes (2,287 words) [view diff] exact match in snippet view article find links to article

{\displaystyle [r^{n}-1]=\{0,1,2,\dots ,r^{n}-1\}} . A cyclic AN code is a principal ideal of the ring [ r n − 1 ] {\displaystyle [r^{n}-1]} . There are integers

Singular trace (3,733 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \liminf _{n\to \infty }{\frac {\psi (2n)}{\psi (n)}}=1.} The principal ideal generated by any compact operator A with μ(A)=ψ' is called the 'small

Loewy decomposition (7,132 words) [view diff] exact match in snippet view article find links to article

_{x}v-{\frac {2}{x-y}}\partial _{y}-{\frac {4}{(x-y)^{2}}}} generating the principal ideal ⟨ L ⟩ {\displaystyle \langle L\rangle } . A first-order factor does