Homomorphism and Isomorphism - ScienceDirectELSEVIERGroup Theory in Quantum Mechanics
Isomorphism: a homomorphism of two morphisms. Two objects are said to be isomorphic if there is an isomorphic mapping between them. Isomorphic objects are indistinguishable in terms of the structure on top of them.满同态（epimorphism）：就是满射的同态。Epimorphism: that's surjective homomorphism....
Special types of homomorphisms have their own names. A one-to-one homomorphism fromGtoHis called amonomorphism, and a homomorphism that is “onto,” or covers every element ofH, is called anepimorphism. An especially important homomorphism is anisomorphism, in which the homomorphism fromGtoHis...
What is homomorphism and isomorphism of group? Isomorphism. Agroup homomorphism that is bijective;i.e., injective and surjective. Its inverse is also a group homomorphism. In this case, the groups G and H are called isomorphic; they differ only in the notation of their elements and are ident...
The homomorphism and isomorphism theorems traditionally taught to students in a group theory or linear algebra lecture are by no means theorems of group theory. They are for a long time seen as general concepts of universal algebra. This article goes even further and identifies them as relational...
Homomorphism and isomorphism are one of the important concepts in algebra. In this paper,on the basis of the concept of( λ,μ)-anti fuzzy normal subgroups,the concept of( λ,μ)-quotient anti fuzzy subgroup is introduced,and the homomorphism and isomorphism of( λ,μ)-anti fuzzy subgroups...
The concepts are in essence the same for Lie algebras as for groups, that is, homomorphisms are structure-preserving mappings and isomorphisms are homomorphisms that are one-to-one. Definition Homomorphic mapping of a Lie algebra L onto a Lie algebra L′ Let ψ be a mapping of a Lie ...
In this paper,we define homomorphisms and isomorphisms of fuzzy groups,and discuss some their properties.We shall mainly prove the decomposition theorems of homomorphisms and isomorphisms,the represatation theorems of homomorphisms and isomorphisms,and the fundamental theorem of homorphisms. 关键词: ...
isomorphismApproximation spacerough setrough grouprough ringrough modulehomomorphismThe theory of rough set is of great advantages in dealing with the ambiguity... QF Zhang,AM Fu,SX Zhao - IEEE 被引量: 5发表: 2009年 Intuitionistic Fuzzy Ring and Its Homomorphism Image homomorphism imageisomorphismOn...
The little book (152 pages) discusses the group axioms, isomorphisms, cyclic groups, coset decompositions, Lagrange 's theorem, permutation groups , normal subgroups , quotient groups, homomorphisms, the first and second isomorphism theorems, and the Jordan - Hölder theorem. 小书( 152页)论述...