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Topologizing Rings of Map Germs: An Order Theoretic Analysis of Germs via Nonstandard Methods
map germ topology nonstandard
2012/6/19
Using nonstandard analysis we define a topology on the ring of germs of functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology is absolutely convex, Hausdorff, that convergent...
Large self-injective rings and the generating hypothesis
Large self-injective rings the generating hypothesis Algebraic Topology
2012/6/9
We construct a number of different examples of non-Noetherian graded rings that are injective as modules over themselves (or have some related but weaker properties). We discuss how these are related ...
Cohomology rings of good contact toric manifolds
contact toric cohomology equivariant cohomology
2011/1/20
A good contact toric manifold M is determined by its moment cone C. We compute the equivariant cohomology ring with Z coefficient of M in terms of the combinatorial data of C. Then under a smoothness ...
Derivations, generic formal fibers and bad Noetherian rings
Derivations generic formal fibers bad Noetherian rings
2010/12/9
We consider a circle of ideas involving differential algebra, local Noetherian rings, and their generic formal fibers. Connecting these ideas gives rise to what we term a “twisted” subring R of a ring...
We introduce the Andr´e-Quillen cohomology of -rings and -rings, this is different to the -ring cohomology defined by Yau in 2005. We show that there is a natural transformation connecting th...