Tag Archives: duals

Commutative Algebra 52

Direct Limits of Rings Let be a directed system of rings. Regard them as a directed system of abelian groups (i.e. ℤ-modules) and take the direct limit A. Proposition 1. The abelian group A has a natural structure of a … Continue reading

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Tensor Product and Linear Algebra

Tensor products can be rather intimidating for first-timers, so we’ll start with the simplest case: that of vector spaces over a field K. Suppose V and W are finite-dimensional vector spaces over K, with bases and respectively. Then the tensor product is the vector … Continue reading

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