Related papers: Canonical and $n$-canonical modules on a Noetheria…
Propositional canonical Gentzen-type systems, introduced in 2001 by Avron and Lev, are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a connective is…
In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…
A good canonical projection of a surface $S$ of general type is a morphism to the 3-dimensional projective space P^3 given by 4 sections of the canonical line bundle. To such a projection one associates the direct image sheaf F of the…
A decorated surface S is a surface with a finite set of special points on the boundary, considered modulo isotopy. Let G be a split reductive group. A pair (G, S) gives rise to a moduli space A(G, S), closely related to the space of G-local…
We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…
We introduce a theory of geometry for nonnoetherian commutative algebras with finite Krull dimension. In particular, we establish new notions of normalization and height: depiction (a special noetherian overring) and geometric codimension.…
We show that for a class of modules over shod algebras, including the canonical tilting modules, the closures of the corresponding orbits in module varieties are regular in codimension one.
Let $R$ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a$ a proper ideal of $R$. We study the invariance of some classes of $\frak a$-relative Cohen-Macaulay modules under pure ring homomorphisms and ring…
The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective finite dimensional algebra is finite. In \cite{Yam}, Yamagata stated the stronger conjecture that the dominant dimension of a non-selfinjective finite…
We study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type. In the domestic case, such tilting modules are constructed by using the technique of universal localization, and they can be…
Let $A$ be an algebra over a commutative ring $R$. If $R$ is noetherian and $A^\circ$ is pure in $R^A$, then the categories of rational left $A$-modules and right $A^\circ$-comodules are isomorphic. In the Hopf algebra case, we can also…
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao…
We study rings which have Noetherian cohomology under the action of a ring of cohomology operators. The main result is a criterion for a complex of modules over such a ring to have finite injective dimension. This criterion generalizes, by…
Let $C$ be a symmetrizable generalized Cartan matrix with symmetrizer $D$ and orientation $\Omega$. In previous work we associated an algebra $H$ to this data, such that the locally free $H$-modules behave in many aspects like…
A criterion is given for a type in a finite rank stable theory to be (almost) internal to a given nonmodular minimal type. The motivation comes from results of Campana which give criteria for compact complex analytic spaces to be algebraic…
For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings.…
We study the canonical basis for the negative part of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras associated to two different matrices satisfying certain conditions may coincide.…
Let $\fa$ denote an ideal of a commutative Noetherian ring $R$ and $M$ and $N$ two finitely generated $R$-modules with $\pd M< \infty$. It is shown that if $\fa$ is principal or $R$ is complete local and $\fa$ a prime ideal with $\dim…
Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan the toric face ring. Assuming that this ring is Cohen-Macaulay, the main result of this paper is to characterize the…
In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.