相关论文: Formally smooth bimodules

Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

We study binomial D-modules, which generalize A-hypergeometric systems. We determine explicitly their singular loci and provide three characterizations of their holonomicity. The first of these states that a binomial D-module is holonomic…

The formal study of completely prime modules was initiated by N. J. Groenewald and the current author in the paper; Completely prime submodules, {\it Int. Elect. J. Algebra}, {\bf 13}, (2013), 1--14. In this paper, the study of completely…

Based on the work done in \cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a…

In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, "virtual" point of view. As natural background for investigating the kind of problems we are dealing with, the virtual…

An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.

Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate…

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…

Certain aspects of Street's formal theory of monads in 2-categories are extended to multimonoidal monads in symmetric strict monoidal 2-categories. Namely, any symmetric strict monoidal 2-category $\mathcal M$ admits a symmetric strict…

It is known that the bi-Lipschitz right classification of function germs admit moduli. In this article we introduce a notion called the Lipschitz simple function germs and present a full classification in the complex case. A surprising…

Let G be a finite group scheme over an algebraically closed field of positive characteristic. Assume further that the connected component of G is unipotent. It is shown that the projectivity of a rational G-module can be detected on a…

Let $A$, $B$ be two rings and $T=\left(\begin{smallmatrix} A & M \\ 0 & B \\\end{smallmatrix}\right)$ with $M$ an $A$-$B$-bimodule. We first construct a semi-complete duality pair $\mathcal{D}_{T}$ of $T$-modules using duality pairs in…

Definition of a smooth action of a CQG on a compact, smooth manifold is given and studied. It is shown that a smooth action is always injective. Furthermore A necessary and sufficient condition for a lift of the smooth action as a bimodule…

In this paper we discuss different properties of noncommutative schemes over a field. We define a noncommutative scheme as a differential graded category of a special type. We study regularity, smoothness and properness for noncommutative…

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…

Let $R$ be a finite ring and let $M, N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As…

Let $A$ be an Artin algebra, $M$ be a Gorenstein projective $A$-module and $B =$ End$_A M$, then $M$ is a $A$-$B$-bimodule. We use the restricted flat dimension of $M_B$ to give a characterization of the homological dimensions of $A$ and…

Skew monoidal categories are monoidal categories with non-invertible `coherence' morphisms. As shown in a previous paper bialgebroids over a ring R can be characterized as the closed skew monoidal structures on the category Mod R in which…

We prove that every mod 2 integral cycle $T$ in a Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by a cycle which is a smooth submanifold $\Sigma$ of nearly the same area, up to a singular set of codimension 3; in…