an induced homomorphism. A homomorphism induced from a map h {\displaystyle h} is often denoted h ∗ {\displaystyle h_{*}} . Induced homomorphisms often...
10 KB (1,329 words) - 18:06, 21 March 2022
of this element. Thus a semigroup homomorphism between groups is necessarily a group homomorphism. A ring homomorphism is a map between rings that preserves...
34 KB (4,199 words) - 00:40, 12 August 2024
¯ c ∗ ( X , A ; G ) {\displaystyle {\bar {H}}_{c}^{*}(X,A;G)} . Induced homomorphism of this cohomology is defined as the Alexander cohomology theory...
12 KB (2,275 words) - 13:02, 22 July 2022
mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function...
12 KB (1,635 words) - 20:10, 2 May 2024
be different.) On the other hand, a module homomorphism M → K is a pure embedding if the induced homomorphism between the tensor products C ⊗ M → C ⊗ K...
6 KB (757 words) - 18:08, 23 May 2023
{\displaystyle [k]} is a ring homomorphism and is called the de Rham homomorphism. Finally, the theorem says that the induced homomorphism [ k ] {\displaystyle...
4 KB (647 words) - 18:08, 25 August 2024
quotient by its torsion subgroup, and sends every homomorphism to the obvious induced homomorphism (which is easily seen to be well-defined). If A is...
7 KB (911 words) - 21:28, 31 July 2024
_{0}(Y)} is bijective, and for every point x in X and every n ≥ 1, the induced homomorphism f ∗ : π n ( X , x ) → π n ( Y , f ( x ) ) {\displaystyle f_{*}\colon...
7 KB (868 words) - 08:22, 10 April 2020
properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a homomorphism from G ∗ H to K. Unless one of the...
9 KB (1,381 words) - 19:13, 11 August 2024
Topological group (section Homomorphisms)
definitions. A homomorphism of topological groups means a continuous group homomorphism G → H. Topological groups, together with their homomorphisms, form a...
50 KB (7,492 words) - 16:51, 25 May 2024
the (usual) Gysin homomorphism induced by the zero-section embedding X ′ ↪ N {\displaystyle X'\hookrightarrow N} . The homomorphism i! encodes intersection...
5 KB (716 words) - 10:14, 27 August 2023
Structure (mathematical logic) (redirect from Homomorphism problem)
substructures are precisely the induced subgraphs. However, a homomorphism between graphs is the same thing as a homomorphism between the two structures coding...
34 KB (5,097 words) - 15:25, 3 July 2024
Then, for a homomorphism f : G → H, (f(u),f(v)) is an arc (directed edge) of H whenever (u,v) is an arc of G. There is an injective homomorphism from G to...
38 KB (4,860 words) - 02:59, 19 August 2024
Flat module (redirect from Faithfully flat ring homomorphism)
characterization of a faithfully flat homomorphism for a not-necessarily-flat homomorphism. Given an injective local homomorphism ( R , m ) ↪ ( S , n ) {\displaystyle...
30 KB (4,590 words) - 03:05, 9 August 2024
Snake lemma (redirect from Connecting homomorphism)
{Gray}\longrightarrow }~\operatorname {coker} c} where d is a homomorphism, known as the connecting homomorphism. Furthermore, if the morphism f is a monomorphism...
9 KB (1,434 words) - 06:56, 10 March 2023
of bits Ω = 2 Z , {\displaystyle \Omega =2^{\mathbb {Z} },} the induced homomorphism is the Baker's map. Consider now the space of functions in y {\displaystyle...
26 KB (4,181 words) - 11:10, 24 July 2024
functional analysis, a topological homomorphism or simply homomorphism (if no confusion will arise) is the analog of homomorphisms for the category of topological...
8 KB (1,458 words) - 12:53, 11 July 2022
{\displaystyle f\colon X\to Y} and a point x in X, consider for any n ≥ 1 the induced homomorphism f ∗ : π n ( X , x ) → π n ( Y , f ( x ) ) , {\displaystyle f_{*}\colon...
4 KB (605 words) - 08:26, 24 May 2022
Hurewicz theorem (redirect from Hurewicz homomorphism)
exists a group homomorphism h ∗ : π n ( X ) → H n ( X ) , {\displaystyle h_{*}\colon \pi _{n}(X)\to H_{n}(X),} called the Hurewicz homomorphism, from the n-th...
9 KB (1,309 words) - 00:36, 19 August 2023
and with composition of loops. The resulting group homomorphism, called the induced homomorphism, is written as π ( f ) {\displaystyle \pi (f)} or, more...
53 KB (8,076 words) - 07:10, 6 August 2024
∗ ( X ) {\displaystyle f^{*}\colon H^{*}(Y)\to H^{*}(X)} is the induced homomorphism in cohomology, then f ∗ ( α ⌣ β ) = f ∗ ( α ) ⌣ f ∗ ( β ) , {\displaystyle...
8 KB (1,292 words) - 06:13, 29 March 2024
Covering group (redirect from Covering homomorphism)
covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering...
12 KB (1,726 words) - 21:24, 30 April 2024
isometries of (T, d), with the quotient space T/π1(Γ) = Γ. Since the induced homomorphism f# is an isomorphism between Fn = π1(Rn) and π1(Γ), we also obtain...
28 KB (4,147 words) - 22:09, 7 July 2024
Functor (redirect from Category homomorphism)
group homomorphisms between free groups. Free constructions exist for many categories based on structured sets. See free object. Homomorphism groups...
24 KB (3,513 words) - 02:56, 11 August 2024
isogeny, provided that f(1A) = 1B. Such an isogeny f then provides a group homomorphism between the groups of k-valued points of A and B, for any field k over...
4 KB (459 words) - 19:45, 24 June 2024
{\textstyle d\neq q} with d ∣ q {\textstyle d\mid q} such that the induced homomorphism χ ~ : ( Z / q Z ) × → C ∗ {\textstyle {\widetilde {\chi }}\colon...
28 KB (3,925 words) - 07:49, 9 June 2024
of bits Ω = 2 Z , {\displaystyle \Omega =2^{\mathbb {Z} },} the induced homomorphism is the Baker's map. The dyadic sequence is then just the sequence...
24 KB (4,718 words) - 20:50, 17 August 2022
continuous maps between spaces induce homomorphisms between relative homology groups. In fact, this map is exactly the induced map on homology groups, but...
11 KB (2,477 words) - 12:00, 16 July 2024
Lie group (redirect from Lie group homomorphism)
continuous homomorphism between real Lie groups turns out to be (real) analytic. The composition of two Lie homomorphisms is again a homomorphism, and the...
64 KB (9,427 words) - 12:29, 18 August 2024
B ) {\displaystyle h\colon (X,A)\rightarrow (Y,B)} , then their induced homomorphisms are the same. Excision: If ( X , A ) {\displaystyle (X,A)} is a...
5 KB (750 words) - 02:45, 7 March 2024