Related papers: An example of Melkersson subcategory which is not …
Let $R$ be a commutative noetherian ring, let $\frak a$ and $\frak b$ be two ideals of $R$; and let $\Ss$ be a Serre subcategory of $R$-modules. We give a necessary and sufficient condition by which $\Ss$ satisfies $C_{\frak a}$ and…
Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In the present paper, we first provide various sufficient (and necessary) conditions for a full subcategory of mod R to be a Serre…
We study two subcategories of the category of artinian modules, a wide subcategory and a Serre subcategory. We prove that all wide subcategories of artinian modules are Serre subcategories. We also provide the bijection between the set of…
We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar way to the author's classification of exact structures of a given additive…
In this paper, we consider subcategories consisting of the extensions of modules in two given Serre subcategories to find a method of constructing Serre subcategories of the category of modules. We shall give a criterion for this…
We construct injective hulls and projective covers in categories of generalized uniform hypergraphs which generalizes the constructions in the category of quivers and the category of undirected graphs. While the constructions are not…
Given a right R-module M and any short exact sequence of right R-modules \[ 0 \to A \to B \to C \to 0, \] it is well known that if both A and C belong to the subinjectivity domain $\mathfrak{\underline{In}^{-1}}(M)$ (resp., the…
We show that the action of the Serre functor on the subcategory of projective-injective modules in a parabolic BGG category $\mathcal O$ of a quasi-reductive finite dimensional Lie superalgebra is given by tensoring with the top component…
Let $k$ be a field of characteristic not $2$. We give a positive answer to Serre's injectivity question for any smooth connected reductive $k$-group whose Dynkin diagram contains connected components only of type $A_n$, $B_n$ or $C_n$. We…
In this work, we propose a new class of jet substructure observables which, unlike fragmentation functions, are largely insensitive to the poorly known physics of hadronization. We show that sub-jet structures provide us with a large…
Let $R$ be a commutative noetherian ring and let $\frak a$ be an ideal of $R$. In this paper, we study a certain condition, namely $C_{\frak a}$, introduced by Aghapournahr and Melkersson, on the extension of two subcategories of…
Every Serre subcategory of an abelian category is assigned a unique type. The type of a Serre subcategory of a Grothendieck category is in the list: $$(0, 0), \ (0, -1), \ (1, -1), \ (0, -2), \ (1, -2), \ (2, -1), \ (+\infty, -\infty);$$…
In this article we give application of closure operators in category of modules. Our main result shows that every subcategory A of injective modules of R-mod (under a mild condition) induces a torsion theory of R-mod.
The shellability of the boundary complex of an unbounded polyhedron is investigated. To this end, it is necessary to pass to a suitable compactification, e.g., by one point. This observation can be exploited to prove that any tropical…
Let C be a subcategory of the category of finitely generated R-modules over a commutative noetheian ring R. We prove that, if C is closed under images and extensions (which we call an IE-closed subcategory), then C is closed under…
Let R be a commutative Noetherian local ring, and denote by mod R the category of finitely generated R-modules. In this paper, we consider when mod R has a nontrivial extension-closed subcategory. We prove that this is the case if there are…
We describe the additive subgroups of fields which are closed with respect to taking inverses. In particular, in characteristic different from two any such subgroup is either a subfield or the kernel of the trace map of a quadratic…
We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$, $D \in {\mathcal C}$ such that $C\ot D$ is semisimple, $C$ and $D$ are semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two…
We generalize a result of Serre's to show that if every vertex of some fixed type of a convex subcomplex of an irreducible spherical building has an opposite, then the subcomplex is completely reducible.
Many Properties of a category X, as for instance the existence of an adjoint or a factorization system, are a consequence of the cowellpoweredness of X. In the absence of cowellpoweredness, for general results, fairly strong assumption on…