Whitehead's original homomorphism is defined geometrically, and gives a homomorphism J : π r ( S O ( q ) ) → π r + q ( S q ) {\displaystyle J\colon \pi _{r}(\mathrm...

of this element. Thus a semigroup homomorphism between groups is necessarily a group homomorphism. A ring homomorphism is a map between rings that preserves...

are the direct sum of the image of the J-homomorphism, and the kernel of the Adams e-invariant, a homomorphism from these groups to Q / Z {\displaystyle...

group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy...

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)...

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...

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...

Monoid homomorphisms are sometimes simply called monoid morphisms. Not every semigroup homomorphism between monoids is a monoid homomorphism, since it...

for any group homomorphism f : G → H {\displaystyle f:G\to H} . Note that f op {\displaystyle f^{\text{op}}} is indeed a group homomorphism from G op {\displaystyle...

conjecture, which is concerned (in one instance) with the image of the J-homomorphism in the stable homotopy groups of spheres. A later paper of Adams and...