Related papers: Finite depth and Jacobson-Bourbaki correspondence

Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every…

We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from…

Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result…

The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent…

Let N_0 \subset N_1 a depth 2, finite index inclusion of type II1 factors and N_0 \subset N_1 \subset N_2 \subset N_3 ... the corresponding Jones tower. D. Nikshych et L. Vainerman built dual structures of quantum C*-groupoid on the…

Let p be a prime. For any finite p-group G, the deep transfers T(H,G'):H/H' --> G'/G'' from the maximal subgroups H of index (G:H)=p in G to the derived subgroup G' are introduced as an innovative tool for identifying G uniquely by means of…

A semidomain is a subsemiring of an integral domain. We call a semidomain $S$ additively reduced if $0$ is the only invertible element of the monoid $(S, +)$, while we say that $S$ is additively Furstenberg if every non-invertible element…

We study necessary and sufficient conditions for a valued field $\KF$ with value group $G$ and residue field $\kf$ (with char $\KF$ = char $\kf$) to admit a truncation closed embedding in the field of generalized power series $\kf((G, f))$…

We prove the existence of a Galois closure for towers of torsors under finite group schemes over a proper, geometrically connected and geometrically reduced algebraic stack $X$ over a field $k$. This is done by describing the Nori…

Let $\varphi\colon\Gamma\to G$ be a homomorphism of groups. In this paper we introduce the notion of a subnormal map (the inclusion of a subnormal subgroup into a group being a basic prototype). We then consider factorizations…

Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the…

We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on…

Let $G$ be a simple simply connected group scheme defined over ${\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p>0$. Moreover, let $B$ be a Borel subgroup of $G$ and $U$ be the unipotent radical of $B$. In this…

The paper studies three classes of Frobenius manifolds: Quantum Cohomology (topological sigma-models), unfolding spaces of singularities (K. Saito's theory, Landau-Ginzburg models), and the recent Barannikov-Kontsevich construction starting…

We characterize finite index depth 2 inclusions of type II_1 factors in terms of actions of weak Kac algebras and weak C*-Hopf algebras. If N\subset M \subset M_1 \subset M_2 \subset ... is the Jones tower constructed from such an inclusion…

Let us consider an algebraic function field defined over a finite Galois extension $K$ of a perfect field $k$. We give some conditions allowing the descent of the definition field of the algebraic function field from $K$ to $k$. We apply…

The notion of an internal preneighbourhood space on a finitely complete category with finite coproducts and a proper $(\mathsf{E}, \mathsf{M})$ system such that for each object $X$ the set of $\mathsf{M}$-subobjects of $X$ is a complete…

We establish a Morita theorem to construct triangle equivalences between the singularity categories of (commutative and non-commutative) Gorenstein rings and the cluster categories of finite dimensional algebras over fields, and more…

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

In this work, we revisit Auslander-Buchweitz Approximation Theory and find some relations with cotorsion pairs and model category structures. From the notions of relatives generators and cogenerators in Approximation Theory, we introduce…