homomorphism in English
He lectured on and wrote up notes on Tate's theorem on homomorphisms between abelian varieties over finite fields.
Use "homomorphism" in a sentence
1. One must not confuse homomorphism with homeomorphism.
2. This excludes the zero homomorphism.
3. Every *-homomorphism is completely positive.
4. In algebra a monomorphism is an injective homomorphism.
5. The image of this homomorphism is the monodromy group.
6. The composition of an antihomomorphism with a homomorphism gives another antihomomorphism.
7. The kernel of a group homomorphism always contains the neutral element.
8. The preimage of a prime ideal under a ring homomorphism is a prime ideal.
9. In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism.
10. Every homomorphism of the Petersen graph to itself that doesn't identify adjacent vertices is an automorphism.
11. Every algebraic structure has its own notion of homomorphism, namely any function compatible with the operation(s) defining the structure.
12. In chapter 1 these properties are derived as necessary conditions for an algebraic and order homomorphism between the real matrices and the floating-point matrices.
13. If the target Y is commutative, then an antihomomorphism is the same thing as a homomorphism and an antiautomorphism is the same thing as an automorphism.
14. First, recall that an additive functor is a functor F: C → D between preadditive categories that acts as a group homomorphism on each hom-set.
15. In chapter 3 these properties are derived as necessary conditions for an algebraic and order homomorphism between the real numbers and a floating-point system.
16. An important role is played in the theory of rings and Algebras, as in any other algebraic theory, by the notions of homomorphism and isomorphism.
17. Chern classes can be used to construct a homomorphism of rings from the topological K-theory of a space to (the completion of) its rational cohomology.
18. In category theory, the concept of catamorphism (from the Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism from an initial algebra into some other algebra.
19. Conversely if ∇ is an affine connection and Γ is such a smooth bilinear bundle homomorphism (called a connection form on M) then ∇ + Γ is an affine connection.
20. In algebraic categories (specifically, categories of varieties in the sense of universal algebra), an isomorphism is the same as a homomorphism which is bijective on underlying sets.
21. If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π1(X, x0), and H1(X) is therefore isomorphic to the abelianization of π1(X, x0).
22. The product of the local reciprocity maps in local class field theory gives a homomorphism of the idele group to the Galois group of the maximal abelian extension of the number or function field.
23. This is equivalent to the above notion, as every dense morphism between two abelian varieties of the same dimension is automatically surjective with finite fibres, and if it preserves identities then it is a homomorphism of groups.
24. Anisogeny(de ned over F q) between elliptic curves E;E0=F q is a rational map ’: E! E0 (x;y) 7! (f(x);yg(x)) for some f;g2F q(x), which is also a group homomorphism
25. The so-called class-invariant homomorphism ψ measures the Galois module structure of torsors—under a finite flat group scheme G—which lie in the image of a coboundary map associated to an isogeny between (Néron models of) abelian varieties with kernel G.
26. A boolean algebra is FREE on the set of generators S iff any map from S to any boolean algebra extends to a unique boolean homomorphism (that is, viewing boolean Algebras as one-object division allegories, it extends to a representation of division allegories).