free module

Let $R$ be a ring.A free module over $R$ is a direct sum of copies of $R$ .

Similarly, as an abelian groupis simply a module over $\\mathbb{Z}$ ,a free abelian groupis a direct sum of copies of $\\mathbb{Z}$ .

This is equivalent to sayingthat the module has a free basis,i.e. a set of elementswith the propertythat every element of the modulecan be uniquely expressedas an linear combination over $R$ of elements of the free basis.

Every free module is also a projective module,as well as a flat module.

单词	FreeModule1
释义	free module Let $R$ be a ring.A free module over $R$ is a direct sum of copies of $R$ . Similarly, as an abelian groupis simply a module over $\\mathbb{Z}$ ,a free abelian groupis a direct sum of copies of $\\mathbb{Z}$ . This is equivalent to sayingthat the module has a free basis,i.e. a set of elementswith the propertythat every element of the modulecan be uniquely expressedas an linear combination over $R$ of elements of the free basis. Every free module is also a projective module,as well as a flat module.
随便看	complete set of primitive orthogonal idempotents CompleteUltrafilterAndPartitions complete ultrafilter and partitions CompleteUltrametricField complete ultrametric field CompleteUniformSpace complete uniform space CompletingTheSquare completing the square Completion completion CompletionOfAMeasureSpace completion of a measure space Complex complex ComplexAnalyticManifold complex analytic manifold ComplexArithmeticgeometricMean complex arithmetic-geometric mean ComplexConjugate complex conjugate ComplexExponentialFunction complex exponential function ComplexFunction complex function