isomorphism n. 同形,同构,类质同像,类质同晶 参考例句: The nature to the drama, is the natural life to the social life, is theorem n.【术语】(尤指数学)定理 first a. 1.第一的;最初的;最早的;最先的;首要的 2.初次的 ad. 1.第一;最初;最先 2.先;首先 3.第一次;首次 4.(用於...
Given a homomorphism between algebras, there exists an isomorphism between the quotient of the domain by its kernel and the subalgebra in the codomain given by its image. This theorem, commonly known as the first isomorphism theorem, is a fundamental algebraic result. Different problems have been...
网络同态定理;第一同构定理 网络释义
(这包括三步:首先验证preserve;然后证明λ是injective的,显然<x-2>+r=0=>r=0;最后显然对任意Q[x]/<x-2>中的元素<x-2>+f,由Division Theorem有它等于<x-2>+r,所以λ是surjective的。证毕) 类比这个过程,我们有 Theorem. (The Fundamental Isomorphism Theorem for Commutative Rings) 事实上这个定理对ar...
(iii) for all i<κ, there is an isomorphism fi:A→Ai such that f↾B=idB. By Proposition 3.14 we have that D admits an HF-ordering < over ∅. Let C⊆D such that cl<(C)=C, B⊆C and |C|<κ. Then there is i<κ such that C∩Ai=B. Then, since C⩽HFD (by Propo...
(the ara/moreno/pardo monoid isomorphism theorem) [ 36 , theorem 7.1] let e be a finite graph. then there is a natural monoid isomorphism v ( l c ( e ) ) ≅ v ( c ∗ ( e ) ) . we conclude our discussion of historical plot line #1 in the development of leavitt path ...
On the other hand, if V = R and if ∆ is chosen quite large, for example ∆ = RR, then the intuition of variables with zero variance strongly suggests that X —> EX should be an isomorphism for suitable V, i.e. that the only V-valued extensive quantities that are so highly hom...
1.2 Graph Isomorphism. 1.3 Vertex Degrees 1.4 Subgraphs and Operations 1.5 Walks, Paths and Connection Chapter 2 Advanced Concepts of Graphs 2.1 Distances and Diameters 2.2 Circuits and Cycles 2.3 Eulerian Graphs 2.4 Hamiltonian Graphs 2.5 Matrix Representations of Graphs ...
can be seen, up to isomorphism, as the group \(g_1\) . 4 pertinent groups here we prove the “only if" part of theorem 3.9 . considering that the arguments used are purely group theoretical, the reading of this section can be postponed to a later time without compromising the ...
induces an isomorphism from to the Lie algebra of primitive elements of , which can be proven using thePBW theorem. Hence Lie algebras embed as a full subcategory of Hopf algebras; that is, they can be thought of as Hopf algebras satisfying certain properties, rather than having extra structu...