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I'm trying to improve my understanding of tensor of products of modules, my algebra background is one semester of undergrad algebra and one semester of graduate algebra, in which I struggled through the section on tensor products. In my graduate course, we used Dummit and Foote and I generally liked their exposition, but found the tensor product section very confusing, so I'm looking for other sources. I'm not interested in anything specific, i.e. not just limited to vector spaces, or $\mathbb{Z}$ modules, although I don't really care about the non-commutative case. Does anyone have any recommendations?

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  • $\begingroup$ What did you find confusing in D&F? Bosch has a nice section on tensor products in his commutative algebra book and basically all of these american general algebra books have a tensor product section iirc. $\endgroup$
    – Qi Zhu
    Commented Jan 3, 2021 at 20:18

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You can read about tensor products all over the place.

The wikipedia page (https://en.wikipedia.org/wiki/Tensor_product_of_modules) is reasonably good and complete if you're looking for a free resource.

Personally, I'm partial to Atiyah and Macdonald's treatment in Chapter 2 of their Commutative Algebra. It has the benefit of being quite to the point and there are some useful and pleasant exercises.

You could also try Algebra by Lang.

Keith Conrad's notes: https://kconrad.math.uconn.edu/blurbs/linmultialg/tensorprod.pdf also appear quite complete, and I've heard good things about the writing.

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  • $\begingroup$ Thanks, I will take a look at those $\endgroup$ Commented Dec 14, 2020 at 1:21

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