Graded Commutative Algebra: A Comprehensive Reference

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SUMMARY

The discussion centers on the search for comprehensive references on graded commutative algebra, specifically regarding graded rings and modules. Participants recommend Eisenbud's "Commutative Algebra" as a valuable resource, noting its utility in understanding graded algebras. The conversation highlights the lack of detailed treatment of modules over preadditive categories in existing texts, including Hartshorne's "Algebraic Geometry." The need for specialized resources that directly address graded structures is emphasized.

PREREQUISITES
  • Understanding of graded rings and modules
  • Familiarity with Eisenbud's "Commutative Algebra"
  • Basic knowledge of Hartshorne's "Algebraic Geometry"
  • Concepts of modules over preadditive categories
NEXT STEPS
  • Research advanced topics in graded commutative algebra
  • Explore Eisenbud's "Commutative Algebra" for specific applications
  • Investigate the theory of modules over preadditive categories
  • Look for specialized texts focusing on graded rings
USEFUL FOR

Mathematicians, algebraists, and graduate students specializing in commutative algebra and those seeking to deepen their understanding of graded structures in algebraic contexts.

Hurkyl
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Is there a good reference for commutative algebra of graded rings and modules?

I've only found little bits and pieces in other texts (e.g. Hartshorne's Algebraic Geometry), and I would like to avoid having to dive fully into the theory of modules over preadditive categories! (And I'd prefer not to have to guess at the right way to generalize definitions & theorems from ordinary commutative algebra)
 
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Modules over preadditive categories? I don't see that in Hartshorne. Are you talking about sheaves of modules?

Anyway, I recommend Eisenbud's Commutative Algebra. I don't know what you specifically want to know about graded algebras, but I'm sure you can find something useful in that book.
 
masnevets said:
Modules over preadditive categories? I don't see that in Hartshorne.
Modules over preadditive categories was a separate thought from the Hartshorne bit. I do have a text on that, but it never specializes any results specifically to graded rings. (It doesn't even do much specialization to ordinary rings!)
 

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