Contents

• 1. Basic definitions
  • 1.1 Monomial orderings
  • 1.2 Examples for monomial orderings
• 2. Standard bases
  • 2.1 Definition
  • 2.2 Standard bases for submodules of free modules
  • 2.3 Basic properties
  • 2.4 Applications
• 3. Solving equations
  • 3.1 Simplification
  • 3.2 Solvability
  • 3.3 Finite solvability
• 4. Syzygies
  • 4.1 Definition
  • 4.2 Resolutions
  • 4.3 Kernel of a module homomorphism
  • 4.4 Module intersection 2
  • 4.5 Ideal quotient
  • 4.6 Saturation
  • 4.7 Annihilator of a module
• 5. Examples
  • 5.1 Ext modules Ext(M,R)
  • 5.2 Hom_R(M,N)
  • 5.3 T¹_X and T¹_X(M)
• Bibliography
• Contents