«HOMOMORPHISM»に関連する英語の本
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1
Foundations of Discrete Mathematics
The constant function from G to H which sends every element of G to the identity
element of H is a homomorphism. It is called the trivial homomorphism. If H is an
abelian group denoted additively, this homomorphism is also called the zero ...
2
Contemporary Abstract Algebra
If (p is a homomorphism from G to H and o is a homomorphism from H to K, show
that orb is a homomorphism from G to K. How are Ker d) and Ker o'qb related? If
<1) and o are onto and G is finite, describe [Ker 0'tb:Ker 4)] in terms of lHl and ...
Let R and S be rings and <p : R — y s a ring
homomorphism. Then every S-
module A can be made into an R -module by defining rx (x e A) to be <p(r)x. One
says that the R-module structure of A is given by pullback along <p. EXAMPLE.
Thomas W. Hungerford, 1974
4
A Concrete Introduction to Higher Algebra
Also associated with a ring Ris U(R), the group of units, or invertible elements, of
R. If f : R → S is a ring homomorphism, then restricting f to the subset U(R) of R
yields a group homomorphism from U(R) to U(S), because f takes the identity ...
5
Lattice Theory: Foundation: Foundation
Let us define a
homomorphism of the semilattice (So; o) into the semilattice (iSi;o)
as a map p : Sq — > Si satisfying p(a o b) = <p(a) o (p(b). Since a lattice £ = (L; V,
A) is a semilattice both under V and under A, we get two
homomorphism ...
A homomorphism of sheaves h : *d — * 33 is a map such that h{Ax) c &3X for all x
6 X and the restriction hx : Ax —* 33x of h to stalks is a homomorphism for all x. A
homomorphism of sheaves induces a homomorphism of the presheaves of ...
7
Elements of Algebra: Geometry, Numbers, Equations
The permutation sign homomorphism. An is the kernel of the sign homomorphism
Sn — » C^ = {1,-1} that sends a permutation a to -1 if a changes the sign of ^(xi, . .
. , xn) and to 1 if it does not (compare with the definition of An in Section 7.5).
8
Graph-based Knowledge Representation: Computational ...
The fundamental notion for studying and using BGs is homomorphism. In the CG
community, a BG homomorphism is traditionally called a projection. We prefer the
term “homomorphism” for two reasons. First, it corresponds to the classical ...
Michel Chein, Marie-Laure Mugnier, 2008
9
A Concrete Introduction to Higher Algebra
If f:G->H is a homomorphism, and if g in G has inverse g'1 so that g*g~l = eG, then
/(g_1) = fig)-1, the inverse of /(g). This follows because eH = /(«e) = /(0 *0-1) = f(g)
*f(g-1), and the inverse of /(g) is unique. We have implicitly seen many ...
10
Lie Groups Beyond an Introduction
The local result is another consequence of the correspondence between analytic
subgroups and Lie subalgebras. In fact, suppose that G and H are analytic
groups and that <p : Q -+ f) is a homomorphism between their Lie algebras. Let 5
= {(X ...
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Cooperative software framework helps tame "too big" data
In GEMS, SPARQL queries are modeled as graph homomorphism routines, enriched with solution modifiers (e.g., sorting, aggregation) to ... «Phys.Org, 3月 15»
Seeing light through others' eyes
A formal power series about the origin is an infinite sum. Homomorphism is an isomorphism if and only if the matrix is inevitable. Advertisement. «Sydney Morning Herald, 12月 11»
