Abstract Let (R,m,k_R) be a regular local k-algebra satisfying the weak Jacobian criterion,
and such that k R/k is an algebraic field extension. Let D_R be the ring of k-linear differential …

Let R be a polynomial ring in n indeterminates with coefficients in the field K of characteristic
p> 0 and 𝒟 be the ring of differential operators over R. In this paper, we introduce the notion …

In this paper we construct a class of homogeneous Hilbert modules over the disc algebra A
(D) as quotients of certain natural modules over the function algebra A (D^ 2). These …

In this paper, at first we give a definition of a generalized total differentiation and A-linear
generalized differentiation and skew-linear generalized differentiation and then we …

We classify regular holonomic D-modules whose characteristic variety is contained in the
union of conormal bundles to the orbits of the group of invertible matrices. The main result is …

Let $ R $ be a graded commutative ring with non-zero unity $1 $ and $ M $ be a graded
unitary $ R $-module. In this article, we introduce the concepts of graded $\phi $-$2 …

We study general Hilbert modules over the disc algebra and exhibit necessary spectral
conditions for the vanishing of certain associated extension groups. In particular, this sheds …

Harish-Chandra defined a homomorphism $\delta:\mathcal {D}(\mathfrak {g})^{G}\to\mathcal
{D}(\mathfrak {h})^{W} $ of algebras of invariant polynomial differential operators. The …

Let $ G $ be a locally compact group. We study the categories of $ L^{\infty}(G) $-comodules
and $ L (G) $-comodules in the setting of dual operator spaces and the associated crossed …

We present three versions of the Lax–Milgram theorem in the framework of Hilbert C^* C∗-
modules, two for self-dual ones over W^* W∗-algebras and one for those over C^* C∗ …