Related papers: About proregular sequences and an application to p…

K. Kato's conjecture about the cohomological Hasse principle for regular connected schemes $\mathfrak X$ which are flat and proper over the complete discrete valuation rings $\mathcal O_N$ of higher local fields $F_N$ is proven. This…

We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $\mathrm{DM}^{\rm adm}(R)$ of \textit{admissible prismatic Dieudonn\'e crystals over $R$} and a natural functor from $p$-divisible groups over…

Given a finitely generated module $M$ over a commutative local ring (or a standard graded $k$-algebra) $(R,\m,k) $ we detect its complexity in terms of numerical invariants coming from suitable $\m$-stable filtrations $\mathbb{M}$ on $M$.…

Endomorphism rings of modules appear as the center of a ring, as the fix ring of ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain *-prime modules (introduced by Bican et…

For a slim, planar, semimodular lattice $L$ and covering square~$S$, G.~Cz\'edli and E.\,T.~Schmidt introduced the fork extension, $L[S]$, which is also a slim, planar, semimodular lattice. We investigate when a congruence of $L$ extends to…

We study the notion of regular singularities for parameterized complex ordinary linear differential systems, prove an analogue of the Schlesinger theorem for systems with regular singularities and solve both a parameterized version of the…

We first give an overview of the basic theory for discrete unital twisted C*-dynamical systems and their covariant representations on Hilbert C*-modules. After introducing the notion of equivariant representations of such systems and their…

By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an equivalence between appropriate subcategories of the module categories of the two rings in the Morita context. These are in fact categories of firm…

Let $\{A_m\}$ be a pro system of associative commutative, not necessarily unital, rings. Assume that the pro systems $\{\mathrm{Tor}^{\mathbb{Z}\ltimes A_m}_i(\mathbb{Z},\mathbb{Z})\}_m$ vanish for all $i>0$. Then we prove that the sequence…

Let $R$ be a commutative ring. An $R$-module $M$ is called a semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal $I$. In this article, we show that the class of semi-regular…

We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…

This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…

We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, $M$ an arbitrary $R$-module and $N$ a finite $R$-module. We prove that \cite[Theorem 2.1]{Mel} and \cite[Proposition 3.3 (i)$\Leftrightarrow$(ii)]{B1} are true for any Serre…

The Mitsch order is already known as a natural partial order for semigroups and rings. The purpose of this paper is to further study of the Mitsch order on modules by investigating basic properties via endomorphism rings. And so this study…

Stable cohomology is a generalization of Tate cohomology to associative rings, first defined by Pierre Vogel. For a commutative local ring $R$ with residue field $k$, stable cohomology modules $\widehat{\mathrm{Ext}}{\vphantom…

All rings are commutative, and all modules are unital. The purpose of this paper is to investigate the characterizations of weakly pseudo primary 2-absorbing sub-module in terms of some types of modules. We provide characterizations for the…

In this work we attempt to generalize our result in [6] [7] for real rings (not just von Neumann regular real rings). In other words we attempt to characterize and construct real closure * of commutative unitary rings that are real. We also…

In this note I define an overconvergent version of prisms and prismatic cohomology as introduced by Bhatt and Scholze and show that overconvergent prismatic cohomology specialises to $p$-adic cohomologies, like Monsky-Washnitzer resp. rigid…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…