By Dagmar M. Meyer
Poincaré duality algebras originated within the paintings of topologists at the cohomology of closed manifolds, and Macaulay's twin structures within the learn of irreducible beliefs in polynomial algebras. those principles are tied jointly utilizing simple commutative algebra concerning Gorenstein algebras. Steenrod operations additionally originated in algebraic topology, yet could most sensible be seen as a way of encoding the data usually hidden at the back of the Frobenius map in attribute p<>0. they supply a noncommutative instrument to review commutative algebras over a Galois box. during this Tract the authors skilfully compile those principles and follow them to difficulties in invariant conception. a few extraordinary and unforeseen interdisciplinary connections are printed that may curiosity researchers within the components of commutative algebra, invariant conception or algebraic topology.
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