Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [9]. Using improved techniques, we show that the Hardy-space analogue of this result holds, and more.

We prove that given a fixed radius r, the maximum density achieved by packings of the hyperbolic plane by radius r circles is the supremum of densities of “periodic packings” (those packings with cofinite symmetry). We also show that the maximal density function is continuous as a function of radius. Our investigations lead us to consider more general questions regarding the density of periodic...

Based on a description of the squares of cofinite primary ideals of A + α (D), we prove the following results: for α ≥ 1, there exists a derivation from A + α (D) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m ∈ N and α ∈ [m, m + 1), every finite-dimensional extension of A + α (D) splits algebraically if and only if α ≥ m + 1/2.

in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $...

The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions (C2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie subalgebra g of the weight one subspace V1 is isomorphic to the irreducible highest weight ĝ-module L(k, 0) for a positive integer k, and V is an integrable ĝ-module. The case in which g is replace...

An elementary proof is given for Hutchinson’s duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.

Let Γ be a nonelementary Kleinian group and H<Γ finitely generated, proper subgroup. We prove that if has finite covolume, then the profinite completions of H are not isomorphic. If index in Γ, there is onto which maps but does not. These results streamline existing proofs exist full-sized groups profinitely rigid absolute sense. They build on circle ideas can used to distinguish among subgroup...