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Are there any good introductory textbooks, preferably with problems, that discuss algebras over a field? I'm hoping for something like a linear algebra textbook, but with an algebra as opposed to a vector space. I haven't come across anything for it, with most introductory-level algebra books building up to Galois rather than algebras. I'd appreciate any leads.

I'm aware of Schafer, but I would like something more general if it exists before delving into non-associative algebras only.

crimthan
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  • I think Schafer's book is already general enough. Associative algebras are a special case, because "non-associative" only means "not necessarily associative". And for associative algebras I would recommend the book by Pierce. For Lie algebras there are again many good books, too, for example the introduction by Humphreys. Other algebras are Leibniz algebras, Malcev algebras, or Novikov algebras. – Dietrich Burde Apr 30 '23 at 09:46
  • @DietrichBurde Thanks for the response. This is all mostly to help me understand Clifford Algebras better (I'm interested in Geometric Algebra more generally), but I've felt all the books I've looked at in the subject have taken the concept of an algebra over a field for granted. So I'll look into Schafer's, thanks! – crimthan Apr 30 '23 at 10:49
  • Then I think you will like the book recommendations here for Geometric Algebra. I am sure that there also $K$-algebras over a field $K$ are explained. Moreover there are references especially for people interested in Clifford algebras. – Dietrich Burde Apr 30 '23 at 11:19
  • @DietrichBurde Unfortunately, I've attempted most of those and a lot of the more mathematically-focused ones seem to require a knowledge of algebra over a field already, and more stuff than I've been able to find. Perhaps it's just that I wasn't mathematically mature enough at the time, but I had worked my way through both Pinter and Dummit and Foote by then but still found them way outside my level and taking a lot for granted... or not really focusing on it as much as I'd want, such as the ones that focused on computer graphics of physics. That's why I was looking a bit more foundational. – crimthan Apr 30 '23 at 14:20

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