Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations

Poincaré duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay''s dual systems in the study of irreducible ideals in polynomial algebras. These two ideas are tied together using basic commutative algebra involving Gorenstein algebras. Steenrod operations also originated in algebraic topology, but may best be viewed as a means of encoding the inf...