Notes in lecture03 - tensor products

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Status	Last Update	Fields
Published	10/25/2023	tensor
Published	10/25/2023	simple tensor
Published	10/25/2023	what does an arbitrary tensor look like
Published	10/25/2023	possible generator of \(M \otimes_R N\)
Published	10/25/2023	Sufficient condition for \(M \otimes_R N\) to be free.
Published	10/25/2023	Example: basis of \(ℂ \otimes_R ℂ\)
Published	10/25/2023	\[ℤ/nℤ \otimes_{{c1::ℤ}} ℚ = 0\]proof
Published	10/25/2023	canonical ‘‘unit’’ isomorphism for tensor product
Published	10/25/2023	canonical ‘‘commutativity’’ isomorphism for tensor product
Published	10/25/2023	canonical ‘‘associative’’ isomorphism for tensors
Published	10/25/2023	canonical ‘‘distributive’’ isomorphism of modules
Published	10/25/2023	invertible module
Published	10/25/2023	\[M \otimes_R R^a \cong {{c1::M^a}}\]\[R^b \otimes_R R^a \cong {{c1::R^{ab}}}\]proof
Published	10/25/2023	\[m \otimes 0 = {{c1::m \otimes (0_R \cdot 0) = 0 \cdot m \otimes 0 = 0 \otimes 0}}\]
Published	10/25/2023	restriction of scalars
Published	10/25/2023	module obtained by extension of scalars
Published	10/25/2023	Universal property of scalar extension
Status	Last Update	Fields