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Longer titles found: Torsion-free abelian group (view)

searching for Free abelian group 28 found (130 total)

Protorus (94 words) [view diff] exact match in snippet view article find links to article

of the circle group), or the Pontryagin dual of a discrete torsion-free abelian group. Some examples of protori are given by solenoid groups. Duocylinder

Cotorsion group (235 words) [view diff] exact match in snippet view article find links to article

a bounded group, that is, a group of bounded exponent. A torsion-free abelian group is cotorsion if and only if it is algebraically compact. Ulm subgroups

Algebraic cycle (1,472 words) [view diff] exact match in snippet view article find links to article

coefficient ni is the multiplicity of Vi. The set of all r-cycles is the free abelian group Z r X = ⨁ V ⊆ X Z ⋅ [ V ] , {\displaystyle Z_{r}X=\bigoplus _{V\subseteq

Adequate equivalence relation (577 words) [view diff] exact match in snippet view article find links to article

rational equivalence form the Chow ring. Let Z*(X) := Z[X] be the free abelian group on the algebraic cycles of X. Then an adequate equivalence relation

Gromov's theorem on groups of polynomial growth (971 words) [view diff] exact match in snippet view article find links to article

quasi-isometric to a finitely generated abelian group contains a free abelian group of finite index. In order to prove this theorem Gromov introduced

Hilton's theorem (495 words) [view diff] exact match in snippet view article find links to article

_{3}\mathbb {Z} _{2}\oplus \mathbb {Z} ^{2}} , i.e. the direct-sum of a free abelian group of rank two with the abelian 2-torsion group with 8 elements. Hilton

Commutator collecting process (470 words) [view diff] exact match in snippet view article find links to article

some total ordering is chosen. Then Fn /Fn+1 is a finitely generated free abelian group with a basis consisting of basic commutators of weight n. Then any

Garnir relations (876 words) [view diff] case mismatch in snippet view article find links to article

each row). The Young tabloid of T is denoted {T}. Now consider the free Abelian group of polytabloids, the formal linear combinations with integer coefficients

Hecke character (1,732 words) [view diff] exact match in snippet view article find links to article

places. Then ψ generates a character χ of the ideal group IS, the free abelian group on the prime ideals not in S. Take a uniformising element π for each

Discrete Morse theory (1,944 words) [view diff] exact match in snippet view article find links to article

boundary operator is the endomorphism ∂ {\displaystyle \partial } of the free abelian group generated by X {\displaystyle {\mathcal {X}}} defined by ∂ ( σ ) =

H-cobordism (1,882 words) [view diff] exact match in snippet view article find links to article

(C_{*},\partial _{*})} by letting C k {\displaystyle C_{k}} be the free abelian group on the k-handles and defining ∂ k : C k → C k − 1 {\displaystyle \partial

Linearly ordered group (1,427 words) [view diff] exact match in snippet view article find links to article

besides the identity. Conversely, F. W. Levi showed that a torsion-free abelian group is bi-orderable; this is still true for nilpotent groups but there

Chow group of a stack (1,446 words) [view diff] exact match in snippet view article find links to article

Chow group is defined exactly as in the classical case: it is the free abelian group generated by integral closed substacks modulo rational equivalence

Stone–von Neumann theorem (3,687 words) [view diff] exact match in snippet view article find links to article

of R, the discrete Heisenberg group is a central extension of the free abelian group Z2n by a copy of Z, and the discrete Heisenberg group modulo p is

Bloch group (1,690 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {Z} (K)=\mathbb {Z} [K\setminus \{0,1\}]} as the free abelian group generated by symbols [x]. Abel's functional equation implies that

Cellular homology (2,866 words) [view diff] exact match in snippet view article find links to article

(n+1)-cells), then H n C W ( X ) {\displaystyle H_{n}^{CW}(X)} is the free abelian group generated by its n-cells, for each n {\displaystyle n} . The complex

Glossary of algebraic geometry (12,488 words) [view diff] exact match in snippet view article find links to article

group A k ( X ) {\displaystyle A_{k}(X)} of a smooth variety X is the free abelian group generated by closed subvarieties of dimension k (group of k-cycles)

Krull ring (2,693 words) [view diff] case mismatch in snippet view article find links to article

is an embedding of A × / U {\displaystyle A^{\times }/U} into the free Abelian group generated by the elements of P {\displaystyle P} . Thus, using the

K3 surface (5,241 words) [view diff] exact match in snippet view article find links to article

The Picard group of a K3 surface X is always a finitely generated free abelian group; its rank is called the Picard number ρ {\displaystyle \rho } . In

Banach–Tarski paradox (6,854 words) [view diff] exact match in snippet view article find links to article

\mathbb {Z} } (if the ratio between the two angles is rational) or the free abelian group over two elements; either way, it does not have the property required

Coherent sheaf (6,934 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X} , K 0 ( X ) {\displaystyle K_{0}(X)} is the quotient of the free abelian group on the set of isomorphism classes of vector bundles on X {\displaystyle

Van Kampen diagram (3,201 words) [view diff] exact match in snippet view article find links to article

following figure shows an example of a Van Kampen diagram for the free abelian group of rank two G = ⟨ a , b | a b a − 1 b − 1 ⟩ . {\displaystyle G=\langle

Presheaf with transfers (2,676 words) [view diff] exact match in snippet view article find links to article

Cor ⁡ ( X , Y ) {\displaystyle \operatorname {Cor} (X,Y)} be the free abelian group generated by elementary correspondences from X to Y; elements of Cor

Mapping class group of a surface (4,595 words) [view diff] exact match in snippet view article find links to article

first homology group H 1 ( S ) {\displaystyle H_{1}(S)} . This is a free abelian group of rank 2 g {\displaystyle 2g} if S {\displaystyle S} is closed of

Fundamental polygon (5,997 words) [view diff] case mismatch in snippet view article find links to article

labelling. The abelianisation of Γ, the quotient group Γ/[Γ, Γ], is a free Abelian group with 2g generators. Thus the genus g is a topological invariant. It

Glossary of algebraic topology (7,621 words) [view diff] exact match in snippet view article find links to article

the singular chain complex of X; i.e., the n-th degree piece is the free abelian group generated by all the maps △ n → X {\displaystyle \triangle ^{n}\to

Glossary of representation theory (5,011 words) [view diff] exact match in snippet view article find links to article

The Kirillov character formula lattice 1. The root lattice is the free abelian group generated by the roots. 2. The weight lattice is the group of all

Glossary of commutative algebra (9,767 words) [view diff] exact match in snippet view article find links to article

fractional ideals. 2. A Weil divisor of a ring is an element of the free abelian group generated by the codimension 1 prime ideals. 3. Cartier divisor divisorial