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) - 02:16, 2 September 2024
homomorphism sometimes means a map which respects not only the group structure (as above) but also the extra structure. For example, a homomorphism of...
10 KB (1,469 words) - 20:01, 25 August 2024
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
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
Kernel (algebra) (redirect from Kernel of a homomorphism)
map defined by the matrix. The kernel of a homomorphism is reduced to 0 (or 1) if and only if the homomorphism is injective, that is if the inverse image...
18 KB (2,553 words) - 15:03, 27 August 2024
composition of module homomorphisms is again a module homomorphism, and the identity map on a module is a module homomorphism. Thus, all the (say left)...
14 KB (2,467 words) - 05:00, 20 June 2024
of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism. The homomorphism theorem is used to prove the isomorphism...
8 KB (1,307 words) - 20:37, 15 March 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
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
of Heinz Hopf (1935). Whitehead's original homomorphism is defined geometrically, and gives a homomorphism J : π r ( S O ( q ) ) → π r + q ( S q ) {\displaystyle...
8 KB (918 words) - 21:06, 22 August 2023