We introduce symmetrizing operators of the polynomial ring A[x] in the variable x over a ring A. When A is an algebra over a field k these operators are used to characterize the monic polynomials F (x) of degree n in A[x] such that A ⊗k k[x](x)/(F (x)) is a free A–module of rank n. We use the characterization to determine the Hilbert scheme parameterizing subschemes of length n of k[x](x). Intr...

The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C*-isomorphisms associated with projections introducing matched triple and semi-harmonious pair of projections. A (P, Q, H) is said be if H a Hilbert C*-module, P Q are on such that their infimum ∧ exists as an element $${\cal L}(H)$$ , where denotes set all adjointable operators H. The C*-subalgebras ...