Extensions of filtered $\lambda$-ring structures over the dual number ring Donald Yau (University of Illinois at Urbana-Champaign), dyau@math.uiuc.edu We study problems related to the existence and uniqueness of filtered $\lambda$-ring structures over the truncated polynomial ring Z[x]/(x^3) that extend a given filtered $\lambda$-ring structure over Z[x]/(x^2).