For a polynomial ring, R, in 4n variables over a field, we consider the submodule of R corresponding to the 4 × 4n matrix made up of n groupings of the linear representation of quarternions with variable entries (which corresponds to the Cauchy-Fueter operator in partial differential equations) and let Mn be the corresponding quotient module. We compute many homological properties of Mn includi...

We present the Maple implementations of two algorithms developed by M. Zhou and F. Winkler for computing a relative Gröbner basis of a finitely generated difference-differential module and we use this to compute the bivariate difference-differential dimension polyomial of the module with respect to the natural bifiltration of the ring of difference-differential operators. An overview regarding ...

For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g Spin(2, 2n+1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest ...

It is shown that the metric on union of sets X and Y defines a Hilbert $C^*$ -module over uniform Roe algebra space with fixed dX. A number examples such -modules are described.

We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group. This has applications to shift-invariant spaces and wavelet theory. One of the main findings in this paper is that whenever a shift-invariant subspace in L2(R...

We present several examples where moments of creators and annihilators on an interacting Fock space may be realized as moments of creators and annihilators on a full Fock module. Motivated by this experience we answer the question, whether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense. We treat the problem in full algebraic generality. As a by-product...

The paper the title refers to is that in Proceedings of the Edinburgh Mathematical Society, 40 (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: 1o to atomize that important result showing by the way connections which are out of favour, 2o to rectify a tiny piece of history. The objective 1o is going to be achieved by adopting means adequate to goals; it is of grea...

This paper finds its motivation in the pursuit of ideals whose local cohomology modules have maximal Hilbert functions. In [8], [9] we proved that the lexicographic (resp. squarefree lexicographic) ideal of a family of graded (resp. squarefree) ideals with assigned Hilbert function provides sharp upper bounds for the local cohomology modules of any of the ideals of the family. Moreover these bo...

The Morita equivalence of m-regular involutive quantales in the context of the theory of Hilbert A-modules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative m-regular involutive quantales are Morita equivalent if and only if they are isomorphic. In the paper [5] F. Borceux and E.M. Vitale made a first step in extending the theory o...