Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Review of Primary decompositions of modules, Associated primes, pri-
mary decompositions in graded Modules.
- Dimension theory, Hilbert function of a graded module, Hilbert-Samuel
polynomial of a local ring, system of parameters and multiplicity.
- Regular sequences, Depth of a module, Cohen-Macaulay module, Macaulay
theorem, Graded depth.
- Stanley-Reisner rings (or face rings ) of simplicial complexes, Hilbert series, h-vectors and f-vectors. Macaulay’s theorem on Hilbert functions. Shellability and Cohen-Macaulayness.
- Partially ordered sets, Möbius functions, Möbius inversion, Eulerian posets,
Shellable posets, Poset rings.
- Local Cohomology of Stanley-Reisner rings and Reisner crietrion for Cohen-
Macaulayness.
- Upper bound theorem.
- Free resolution of monomial ideals.
- H. Matsumura, Commutative ring theory, Cambridge University Press, 1986.
- W. Bruns And J. Herzog, Cohen-Macaulay Rings (Revised edition), Cambridge University Press, 1998.
- S. R. Ghorpade, A R Shastri, M K Srinivasan and J K Verma(Editors), Combinatorial Topology and Algebra, Lecture notes Series 18, Ramanujan Mathematical Society 2013.
- E. Miller and B. Sturmfels, Combinatorial commutative algebra, GTM-227,
Springer, 2004.
- J. Herzog and T. Hibi, Monomial Ideals, GTM-260, Springer, 2011.
- Balwant Singh, Basic Commutative Algebra, World Scientific, 2013.
- R. H. Villarreal, Monomial Algebra, Marcel Dekker, 2001.
