Related papers: Generalized Rank via Minimal Subposet

Let $M$ be a finite module and let $I$ be an arbitrary ideal over a Noetherian local ring. We define the generalized Hilbert function of $I$ on $M$ using the 0th local cohomology functor. We show that our definition re-conciliates with that…

Let $G$ be a finite group, and $C$ be an abelian group. We introduce the notions of $C$-monomial $G$-sets and $C$-monomial $G$-posets, and state some of their categorical properties. This gives in particular a new description of the…

Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…

A subset $S$ of vertices of a graph $G$ is a \emph{general position set} if no shortest path in $G$ contains three or more vertices of $S$. In this paper, we generalise a problem of M. Gardner to graph theory by introducing the \emph{lower…

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for…

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for c not equal to c'. If we keep in place the latter axiom but allow for more…

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…

Let $G\subset\hat{G}$ be two complex connected reductive groups. We deals with the hard problem of finding sub-$G$-modules of a given irreducible $\hat{G}$-module. In the case where $G$ is diagonally embedded in $\hat{G}=G\times G$, S.…

Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g\geq 6$ and $Y$ has genus at most $2g-1$; in addition, suppose that $Y$ is not closed if it has genus $2g-1$. Our main result asserts that every…

In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous…

Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts…

Let $\mathcal{C}$ be a small category. We investigate ringed sites $(\mathbf{C},\mathfrak{R})$ on $\mathcal{C}$ and the resulting module categories $\mathfrak{M}{\rm od}\text{-}\mathfrak{R}$. When $\mathcal{C}$ is finite, based on…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

To every local complete intersection ring one may associate a so-called generic hypersurface. In this paper we introduce rank varieties for modules and complexes over the generic hypersurface. The definition uses extension of scalars,…

Let $F$ be a global field, $A$ a central simple algebra over $F$ and $K$ a finite (separable or not) field extension of $F$ with degree $[K:F]$ dividing the degree of $A$ over $F$. An embedding of $K$ in $A$ over $F$ exists implies an…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…

We prove that the arithmetic degree of a graded or local ring is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideals $I$ in $A$. In particular, if $Spec (A)$ is equidimensional and has an…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We…