Moduli space of filteredλ-ringstructures over a filtered ring

Donald Yau
2004 International Journal of Mathematics and Mathematical Sciences  
Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filteredλ-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series ringsR[[x]], whereRis betweenℤandℚ, with thex-adic filtration, we mimic the construction of the Lazard ring in formal group theory and show
more » ... up theory and show that the set of filteredλ-ring structures overR[[x]]is canonically isomorphic to the set of ring maps from some "universal" ringUtoR. From a local perspective, we demonstrate the existence of uncountably many mutually nonisomorphic filteredλ-ring structures over some filtered rings, including rings of dual numbers over binomial domains, (truncated) polynomial, and power series rings overℚ-algebras.
doi:10.1155/s0161171204304138 fatcat:ldy35xydtjh53gom63lwv3tnzi