“Substructure”的概念、定义、习题解题方法及翻译-数学辞典

单词	Substructure
释义	substructure Let $\\Sigma$ be a fixed signature, and $\\mathfrak{A}$ and $\\mathfrak{B}$ structures for $\\Sigma$ . We say $\\mathfrak{A}$ is a substructure of $\\mathfrak{B}$ , denoted $\\mathfrak{A}\\subseteq\\mathfrak{B}$ , if for all $x\\in\\mathfrak{A}$ we have $x\\in\\mathfrak{B}$ , and the inclusion map $i\\colon\\mathfrak{A}\\to\\mathfrak{B}:x\\mapsto x$ is an embedding. When $\\mathfrak{A}$ is a substructure of $\\mathfrak{B}$ , we also say that $\\mathfrak{B}$ is an extension of $\\mathfrak{A}$ . A submodel $\\mathfrak{A}$ of a model $\\mathfrak{B}$ of a (first-order) language $\\mathcal{L}$ if $\\mathfrak{A}$ is a model of $\\mathcal{L}$ and $\\mathfrak{A}$ is a substructure of $\\mathfrak{B}$ .
随便看	proof of Wilson’s theorem using the Wilson quotient ProofOfYoungInequality proof of Young Inequality ProofOfYoungsInequalityByPicture proof of Young’s inequality by picture ProofOfZermelosPostulate ProofOfZermelosWellorderingTheorem proof of Zermelo’s postulate proof of Zermelo’s well-ordering theorem proof of ◇ is equivalent to ♣ and continuum hypothesis ProofThat3IsTheOnlyPrimePerfectTotientNumber proof that 3 is the only prime perfect totient number ProofThat4xExceedsTheProductOfThePrimesUpToX proof that 4^x exceeds the product of the primes up to x ProofThatACompactSetInAHausdorffSpaceIsClosed proof that a compact set in a Hausdorff space is closed ProofThatADomainIsDedekindIfItsIdealsAreInvertible proof that a domain is Dedekind if its ideals are invertible ProofThatADomainIsDedekindIfItsIdealsAreProductsOfMaximals proof that a domain is Dedekind if its ideals are products of maximals ProofThatADomainIsDedekindIfItsIdealsAreProductsOfPrimes proof that a domain is Dedekind if its ideals are products of primes ProofThatAEuclideanDomainIsAPID proof that a Euclidean domain is a PID proof that a finite abelian group has element with ERROR(\delimiter)⁢69640972⁢g⁢ERROR(\delimiter)⁢86418188=e⁢x⁢p(G)

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

substructure