Related papers: Projective systemic modules
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…
The concept of multialgebraic structure -- an "algebraic like" structure but endowed with multiple valued operations -- has been studied since the 1930's; in particular, the concept of hyperrings was introduced by Krasner in the 1950's.…
We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by…
We describe Koszul type complexes associated with a linear map from any module to a free module, and vice versa with a linear map from a free module to an arbitrary module, generalizing the classical Koszul complexes. Given a short complex…
We adapt the notion of an algebraic theory to work in the setting of quasicategories developed recently by Joyal and Lurie. We develop the general theory at some length. We study one extended example in detail: the theory of commutative…
Let $R$ be a ring and $S$ a multiplicative subset of $R$. An $R$-module $P$ is called uniformly $S$-projective provided that the induced sequence $0\rightarrow \mathrm{Hom}_R(P,A)\rightarrow \mathrm{Hom}_R(P,B)\rightarrow…
Let R be a commutative ring and C a semidualizing R-module. In this article, we introduce and investigate the notion of DC-projective complexes. We first prove that a complex X is DC-projective if and only if each degree of X is a…
We study the geometry of tropical extensions of hyperfields, including the ordinary, signed and complex tropical hyperfields. We introduce the framework of 'enriched valuations' as hyperfield homomorphisms to tropical extensions, and show…
In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct…
We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…
The classical construction of the Weil representation, with complex coefficients, has long been expected to work for more general coefficient rings. This paper exhibits the minimal ring $\mathcal{A}$ for which this is possible, the integral…
The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…
We study support $\tau$-tilting modules over preprojective algebras of Dynkin type. We classify basic support $\tau$-tilting modules by giving a bijection with elements in the corresponding Weyl groups. Moreover we show that they are in…
We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…
Based on the work done in \cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a…
We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…