Def. Ring Homomorphism/IsomorphismA ring homomorphism \phi from a ring R to a ring S is a mapping from R to S that preserves the two ring operations; that is, for all a,b \in R : \phi(a+b) = \phi(a)…
Show that a homomorphism from a field onto a ring with more that one element must be an isomorphism. Answer: \phi:F \rightarrow R Let \phi(a) = \phi(b) , suppose a \not = b , then \phi(a-b) = 0 Let c = a-b , c \not = 0 , then \langle c \rangle \subset Ker...
A ring homomorphism of R 1 to R 2 is a function φ : R 1 → R 2 which preserves multiplication i.e. φ (rs) = φ (r) φ (s) and φ (r + s) = φ (r) + φ (s) for all r, s ∈ R 1 . A ring isomorphism is a ring homomorphism that is one-to-one and onto. ...
homomorphism imageisomorphismOn the basis of intuitionistic fuzzy sets defined by K.Atanassov, we define intuitionistic fuzzy ring, then we discuss its basic... LM Yan - IEEE 被引量: 5发表: 2009年 Homomorphisms and Rigid Isomorphisms of Twisted Group Doubles We prove several results concerning ...
Lets cover some background around Chinese Remaindering and homomorphisms of rings – Consider , a monic polynomial of degree N that splits into r distinct irreducible factors of degree d = N/r, viz. . (In the case of mod 2 we have . Let denote the ring which is the quotient of modu...
Then the Skolem–Noether Theorem gives a relationship between any two homomorphisms of a simple subalgebra into a simple algebra whose center coincides with the underlying field of scalars. Section 8 proves the Double Centralizer Theorem, which says for this situation that the centralizer of the ...
(A) to be quasi-Frobenius: Qℓ(A) is quasi-Frobenius if and only if A satisfies the ascending chain condition for left I(AA)-annihilators and rA(L) = 0 for any left ideal L of A such that there is an A-homomorphism from L to A which is not extended properly to any left ...
then there exists a unique maximal ideal M of R called the crucial maximal ideal of R ⊂ S such that the canonical injective ring homomorphism RM⟶SM can be viewed as a minimal ring extension, while the canonical ring homomorphism RQ⟶SQ is an isomorphism for all prime ideals Q of R...
Especially,several theorems of homomorphism and isomorphism of regular power ring are established. 随着模糊数学的发展 ,各种代数结构的提升已显得越来越重要 ,李洪兴教授在文[1,2 ]中首次提出并研究了幂群及HX环 ,本文在文 [3～ 6 ]的基础上深入讨论了幂环的一些性质 ,并在正则幂环中建立了几个同态与同...
The theorems of homomorphism and isomorphism ahoutfuzzy power ringand power ring are established,setting a foundation for further studyingfuzzy power ringand power ring. 建立了模糊幂环或幂环上的同态与同构定理,它为进一步研究模糊幂环或幂环奠定了基础 ...