“GrouplikeElements”的概念、定义、习题解题方法及翻译-数学辞典

单词	GrouplikeElements
释义	grouplike elements Let $(C,\\Delta,\\varepsilon)$ be a coalgebra over a field $k$ . Definition. The element $g\\in C$ is called grouplike iff $g\eq 0$ and $\\Delta(g)=g\\otimes g$ . The set of all grouplike elements in a coalgebra $C$ is denoted by $G(C)$ . Properties. $0)$ The set $G(C)$ can be empty, but (for example) if $C$ can be turned into a bialgebra, then $G(C)\eq\\emptyset$ . In particular Hopf algebras always have grouplike elements. $1)$ If $g\\in G(C)$ , then it follows from the counit property that $\\varepsilon(g)=1$ . $2)$ It can be shown that the set $G(C)$ is linearly independent.
随便看	proof of finite extensions of Dedekind domains are Dedekind ProofOfFiniteInseparableExtensionsOfDedekindDomainsAreDedekind proof of finite inseparable extensions of Dedekind domains are Dedekind ProofOfFinitelyGeneratedTorsionfreeModulesOverPruferDomains proof of finitely generated torsion-free modules over Prüfer domains ProofOfFiniteSeparableExtensionsOfDedekindDomainsAreDedekind proof of finite separable extensions of Dedekind domains are Dedekind ProofOfFirstIsomorphismTheorem proof of first isomorphism theorem ProofOfFixedPointsOfNormalFunctions proof of fixed points of normal functions ProofOfFodorsLemma proof of Fodor’s lemma ProofOfFourthIsomorphismTheorem proof of fourth isomorphism theorem ProofOffracftfstsleqfracfufsusleqfracfuftutForConvexF ProofOfFrattiniArgument proof of Frattini argument ProofOfFrobeniusReciprocity proof of Frobenius reciprocity ProofOfFubinisTheoremForTheLebesgueIntegral proof of Fubini’s theorem for the Lebesgue integral ProofOfFunctionalEquationForTheThetaFunction proof of functional equation for the theta function ProofOfFunctionalMonotoneClassTheorem

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。

grouplike elements