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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 (241 total)

alternate case: principal ideal

Solid set (383 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 (550 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) (1,762 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

Janaki Ramayana (341 words) [view diff] exact match in snippet view article find links to article

version of Ramayana in poetic form composed by considering Sita as the principal ideal character. In the Indian Subcontinent Ramayana is written in different

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

Divisible group (1,422 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

Completeness (order theory) (1,914 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

Tangent cone (1,148 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

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 (2,326 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

Hilbert symbol (1,645 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

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 (4,204 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 (18,671 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

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

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

Inverse semigroup (3,739 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

Éléments de mathématique (3,110 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:

Pell's equation (6,689 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 (548 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) (2,509 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

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}

Glossary of category theory (11,754 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

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 (2,372 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