-
exact after tensoring, a pure
submodule defines a
short exact sequence (known as a pure
exact sequence) that
remains exact after tensoring with any module...
-
functors at X. This
functor EX is exact.
While tensoring may not be left exact, it can be
shown that
tensoring is a
right exact functor: Theorem: Let A,B...
- ⊗ A {\displaystyle B\otimes A} , the
distinction between tensoring on the left and
tensoring on the
right becomes immaterial, so
every right closed braided...
- I^{k}}
kills A / ( a + I k ) {\displaystyle A/({\mathfrak {a}}+I^{k})} ),
tensoring the
above with M {\displaystyle M} , we get: 0 → a / ( I k ∩ a ) ⊗ M →...
- the
natural map from the
tensor product C ⊗ A to B ⊗ A is injective.
Tensoring an
abelian group A with Q (or any
divisible group)
kills torsion. That...
- f(x)\otimes g(y)\end{cases}}} The
construction has a
consequence that
tensoring is a functor: each
right R-module M
determines the
functor M ⊗ R − : R...
-
saying the
manifold is
complex (which is what the
chart definition says).
Tensoring the
tangent bundle with the
complex numbers we get the
complexified tangent...
-
summands of free modules. Flat
modules are
defined by the
property that
tensoring with them
preserves exact sequences. Torsion-free
modules form an even...
-
presentation is
useful for com****tion. For example,
since tensoring is right-exact,
tensoring the
above presentation with a module, say N, gives: ⨁ i ∈...
- It
captures the
algebraic essence of
tensoring,
without making any
specific reference to what is
being tensored. Thus, all
tensor products can be expressed...
