Projective bundle ideals and Poincaré duality algebras

The study of maximal–primary irreducible ideals in a commutative graded connected Noetherian algebra over a field is in principle equivalent to the study of the corresponding quotient algebras. Such algebras are Poincaré duality algebras. A prototype for such an algebra is the cohomology with field coefficients of a closed oriented manifold. Topological constructions on closed manifolds often lead to algebraic constructions on Poincaré duality algebras and therefore also on maximal–primary irreducible ideals. It is the purpose of this note to examine several of these and develop some of their basic properties.