Related papers: Graded Bourbaki ideals of graded modules

Let $A$ be an associative unital algebra, $B_k$ its successive quotients of lower central series and $N_k$ the successive quotients of ideals generated by lower central series. The geometric and algebraic aspects of $B_k$ and $N_k$ have…

We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…

Let $R$ be a commutative Noetherian ring graded by a torsionfree abelian group $G$. We introduce the notion of $G$-graded irreducibility and prove that $G$-graded irreducibility is equivalent to irreducibility in the usual sense. This is a…

This paper systematically develops a notion of regular sequences in the context of $R$-linear triangulated categories for a graded-commutative ring $R$. The notion has equivalent characterizations involving Koszul objects and local…

In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and…

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

In this paper, we shall describe the graded canonical module of a Noetherian multi-section ring of a normal projective variety. In particular, in the case of the Cox ring, we prove that the graded canonical module is a graded free module of…

Let $R$ be a commutative Noetherian ring. Using the new concept of linkage of ideals over a module, we show that if $\mathfrak{a}$ is an ideal of $R$ which is linked by the ideal $I$, then $cd(\mathfrak{a},R) \in \{ grad \mathfrak{a},…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded primary-like submodules as a new generalization of graded primary ideals and give…

In the first part of this paper the projective dimension of the structural modules in the BGG category $\mathcal{O}$ is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an…

For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the…

We give lower and upper bounds on the Buchsbaum-Rim multiplicity of finitely generated torsion-free modules over two-dimensional regular local rings, and conditions for them to attain the bounds. As consequences, we have formulae on the…

Let $k$ be a unital commutative ring. In this paper, we study polynomial functors from the category of finitely generated free nilpotent groups to the category of $k$-modules, focusing on comparisons across different nilpotency classes and…

Let $\mathcal{R}$ be a free Lie conformal algebra of rank $2$ with $\mathbb{C}[\partial]$-basis $\{L,I\}$ and relations \begin{eqnarray*} \left[L_{\lambda} L\right]=(\partial+2 \lambda) (L+I),\ \left[L_{\lambda} I\right]=(\partial+\lambda)…

This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrically weighted graded modules of such modular forms, where the…

Let $R$ be a commutative ring and $I\subset R$ a finitely generated ideal. We discuss two definitions of derived $I$-adically complete (also derived $I$-torsion) complexes of $R$-modules which appear in the literature: the idealistic and…

We study the blowup algebras of the modules that are direct sums of ideals generated by either maximal minors of a ladder matrix or unit interval determinantal ideals. Specifically, we determine Gr\"{o}bner bases for the presentation ideals…

We show that high Veronese subrings of any commutative graded ring have a Grobner basis with all relations of degree 2. (The d-th Veronese subring of a ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means we take…

Let $R$ be a positively graded algebra over a field. We say that $R$ is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical…

Minimal free resolutions of graded modules over a noetherian polynomial ring have been attractive objects of interest for more than a hundred years. We introduce and study two natural extensions in the setting of graded modules over a…