A while back a topologist friend asked me why the set of prime ideals of a ring deserved to be singled out for study. Another friend, a symplectic geometer, asked why anyone would want to put a scheme structure on the paramaters that classify a type of object (i.e. construct a moduli space). Algebraic geometry does have a reputation for being somewhat impenetrable (and I won’t say it’s undeserv...

The spectral sequence associated to the Arone-Goodwillie tower for the n-fold loop space functor is used to show that the first two non-trivial layers of the nilpotent filtration of the reduced mod 2 cohomology of a (sufficiently connected) space with nilpotent cohomology are comparable. This relies upon the theory of unstable modules over the mod 2 Steenrod algebra, together with properties of...

In this paper algebras with identity, over ordered fields, which possess a (weak) submultiplicative positive bilinear form are studied. They are called (weak) subdecomposition algebras. It is proved that every weak subdecomposition algebra is a simple quadratic algebra with no nontrivial nilpotents or idempotents. If a weak subdecomposition algebra is also flexible, then it is a noncommutative ...