Related papers: The relationships between Invertible Module Maps X…

Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The…

For some involutive maps $\Phi:{\mathbb C}P^1 \times {\mathbb C}P^1 \to {\mathbb C}P^1 \times {\mathbb C}P^1$ we find all invariants with separated variables. We investigate a link of the maps and their invariants with separated variables…

Commutative rings in which every prime ideal is the intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that {\it classical prime} submodules are the…

A Hilbert space operator $A\in\B$ is left $(X,m)$-invertible by $B\in\B$ (resp., $B\in\B$ is an $(X,m)$-adjoint of $A\in\B$) for some operator $X\in\B$ if…

For a commutative noetherian ring R, we investigate relations between tilting and cotilting modules in Mod-R and Mod-R_m where m runs over the maximal spectrum of R. For each finite n, we construct a 1-1 correspondence between (equivalence…

We consider a class of so-called ring $Q$-mappings that are a generalization of quasiconformal mappings. Theorems on the local behavior of inverse maps of this class are obtained. Under certain conditions, we also investigated the behavior…

In the present paper, we construct two classes of non-weight modules $\Omega(\lambda,\alpha,\beta)\otimes\mathrm{Ind}(M)$ and $\mathcal{M}\big(V,\Omega(\lambda,\alpha,\beta)\big)$ over the twisted Heisenberg-Virasoro algebra, which are both…

Let $R$ be a ring with involution. The recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary $*$-ring case. It is shown that the group, Moore-Penrose, core and dual core inverse are closely…

Let A be an algebra in a variety V. We study the modulization of a pointed A-overalgebra P, show that it is totally in any variety that P is totally in, and apply this theory to the construction of the enveloping ringoid Z[A,V].

In this article, we explore the problem of constructing high-dimensional expanders through the study of relations between expansion constants over different rings. We investigate expansion constants of integer matrices regarded as morphisms…

We investigate generalized inverses of matrices associated with two classes of digraphs: double star digraphs and D-linked stars digraphs. For double star digraphs, we determine the Drazin index and derive explicit formulas for the Drazin…

Let $X$ be a smooth projective variety. We show that the map that sends a codimension one distribution on $X$ to its singular scheme is a morphism from the moduli space of distributions into a Hilbert scheme. We describe its fibers and,…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…

Let $(R, \mathfrak m)$ be a commutative noetherian local ring and $I$ an ideal of $R$. For every $R$-module $M$, $\gamma_I(M) = \sum\{ \operatorname{Bi} f \,|\, f \in \operatorname{Hom}_R(I,M)\}$ is called the trace of $I$ in $M$. It is…

We provide the definition and fundamental properties of algebraic elements with respect to an operator satisfying hypothesis (h). Furthermore, we analyze Hilbert modules using C_0-operators relative to a bounded finitely connected region…

Around 1990 Soibelman constructed certain irreducible modules over the quantized coordinate algebra. A. Kuniba, M. Okado, Y. Yamada recently found that the relation among natural bases of Soibelman's irreducible module can be described…

It is known that the variety parametrizing pairs of commuting nilpotent matrices is irreducible and that this provides a proof of the irreducibility of the punctual Hilbert scheme in the plane. We extend this link to the nilpotent commuting…

Let $G$ be a connected reductive group. We find a necessary and sufficient condition for a quasiaffine homogeneous space of $G$ to be embeddable into an irreducible $G$-module. In addition, for an affine homogeneous space we find a…

We prove orientation results for evaluation maps of moduli spaces of rational stable maps to del Pezzo surfaces over a field, both in characteristic $0$ and in positive characteristic. These results and the theory of degree developed in a…