Related papers: Similar submodules and coincidence site modules
It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case…
In our recent work, we introduced a generalization of the prime ideal factorization in Dedekind domains for submodules of finitely generated modules over Noetherian rings. In this article, we find conditions for the intersection of two…
Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the…
We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the…
The Springer modules have a combinatorial property called ``coincidence of dimensions,'' i.e., the Springer modules are naturally decomposed into submodules with common dimensions. Morita and Nakajima proved the property by giving modules…
We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…
This is the extended version of the paper "Special Lagrangian conifolds, I: Moduli spaces", which discusses the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the…
We discuss the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. This category allows for…
The theory of factor-equivalence of integral lattices establishes a far-reaching relationship between the Galois module structure of the unit group of the ring of integers of a number field and its arithmetic. For a number field $K$ that is…
This paper has two objectives. First, we study lattices with skew-Hermitian forms over division algebras with positive involutions. For division algebras of Albert types I and II, we show that such a lattice contains an "orthogonal" basis…
While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…
Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary forms of degree $d$--labelled by partitions of $d$. Given a partition $\lambda$, let $X_\lambda$ be the set of forms with root multiplicity corresponding to $\lambda$.…
Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…
We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles,…
We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.
Given a multiplicatively closed subset $S$ of the integers, there exist Structure Theorems for $LC$ modules over the localization $\mathbb{Z}S^{-1}$ that are "similar" to those of $LCA$ groups. The most notable one is the 1st Theorem: Given…
The first aim of this work is to characterize when the lattice of all submodules of a module is a direct product of two lattices. In particular, which decompositions of a module $M$ produce these decompositions: the \emph{lattice…
We provide and motivate in this paper a natural framework for the study of approximate lattices. Namely, we consider approximate lattices in so-called $S$-adic linear groups and define relevant notions of arithmeticity. We also adapt to…
This work is motivated by an investigation into whether, and if so how, certain well known facts about Lie groups manifest in the context of group schemes over rings of integers of local fields. There are the following well-known relations…
We consider abelian length categories, a generalization of module categories over Artin algebras. Let $\mathcal{A}$ be an abelian length category of colocal type. We show that the lattice $\mathsf{S}(\mathcal{A})$ of full additive subobject…