Nov 15, 2026  
Spring 2027 Graduate Catalog 
    
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Spring 2027 Graduate Catalog
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MAT 544 - Commutative and Homological Algebra

An introduction to the techniques of commutative and homological algebra useful in algebra, algebraic geometry, number theory, and related fields. Review of rings and modules, tensor products and localization. Spectrum of prime ideals, Noetherian and Artinian rings and modules, completion, dimension theory, local rings, discrete valuation rings and Dedekind domains, integral dependence. Chain complexes, projective and injective resolutions, examples of derived functors (Ext and Tor), basic category theory (adjoint functors, natural transformations, limits and colimits), abelian categories.

3 credits

Prerequisite(s): MAT 535 

Grading Letter graded (A, A-, B+, etc.) ​

Offered Fall


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