Cornell Math - MATH 739, Spring 1999

MATH 739 — Spring 1999
Topics in Algebra II

Instructor: Irena Peeva

Time:  TR 2:55-4:10

Room: WE B25

 

Commutative Algebra is the theory of commutative rings and their modules. The lectures will cover different topics and will have different perspective than those in MATH 634. The basic concepts of Commutative Algebra (such as prime ideals, primary decomposition, localization, and dimension theory) will be introduced and no background in MATH 634 will be required.

The lectures will emphasize the connections of Commutative Algebra to Algebraic Geometry, Combinatorics, and Homological Algebra:

  • many definitions and results in Commutative Algebra are motivated by geometric ideas and have deep applications in Algebraic Geometry
     
  • there are close connections between certain topics in Commutative Algebra and in Combinatorics; for example, Hilbert functions and f,h-vectors, monomial resolutions and topology of subspace arrangements, homology of monomial or toric ideals and homology of simplicial complexes
     
  • Homological Algebra provides some of the main tools used in Commutative Algebra; for example, complexes, Tor-groups, Ext-groups, exact sequences, and spectral sequences.

Prerequisites: A good background in abstract algebra.

Textbooks:
D. Eisenbud, Commutative Algebra, Springer 1994
M. Atiyah and I. MacDonald, Introduction to Commutative Algebra, Addison Wesley 1969
H. Matsumura, Commutative ring theory, Cambridge University Press 1986.