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 ...

We construct quantum commutators on module-algebras of quasitriangular Hopf algebras. These are quantum-group covariant, and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy a generalized Jacobi identity, turning the modulealgebra into a quantum-Lie algebra. The purpose of this short communication is to present a quantum commutato...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

Rogosa, Morrison (National Institute of Dental Research, Bethesda, Md.), and Ferial S. Bishop. The genus Veillonella. III. Hydrogen sulfide production by growing cultures. J. Bacteriol. 88:37-41. 1964.-The conditions necessary for H(2)S production by 105 strains of Veillonella, from a variety of sources and comprising seven anti-genic groups, are presented and discussed. All strains, during 1 t...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

Let G be a finite group. It is well known that a Mackey functor {H 7→ M(H)} is a module over the Burnside ring functor {H 7→ Ω(H)}, where H ranges over the set of all subgroups of G. For a fixed homomorphism w : G → {−1, 1}, the Wall group functor {H 7→ Ln(Z[H], w|H)} is not a Mackey functor if w is nontrivial. In this paper, we show that the Wall group functor is a module over the Burnside rin...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.

In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...

A few years ago, I defined a squarefree module over a polynomial ring S = k[x1, . . . , xn] generalizing the Stanley-Reisner ring k[∆] = S/I∆ of a simplicial complex ∆ ⊂ 2. This notion is very useful in the StanleyReisner ring theory. In this paper, from a squarefree S-module M , we construct the k-sheaf M on an (n − 1) simplex B which is the geometric realization of 2. For example, k[∆] is (th...