Related papers: A characterisation of higher torsion classes

In extended hearts of bounded $t$-structures on a triangulated category, we provide a Happel-Reiten-Smalo tilting theorem and a characterization for $s$-torsion pairs. Applying these to $m$-extended module categories, we characterize…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

We prove that the Auslander class determined by a semidualizing module is the left half of a perfect cotorsion pair. We also prove that the Bass class determined by a semidualizing module is preenveloping.

We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair ($\mathcal T$, $\mathcal F$) of full replete subcategories in a category $\mathcal C$, the corresponding full subcategory…

Torsion theories play an important role in abelian categories and they have been widely studied in the last sixty years. In recent years, with the introduction of pretorsion theories, the definition has been extended to general…

In this paper, we study the torsion subgroup, which is denoted by ${\rm TK}_1(E)$, of the Whitehead group $E^*/[E^*,E^*]$ of a graded division algebra $E$ which is finite dimensional over its center. In particular, we provide formulas for…

Let $\mathcal B$ be an extriangulated category with enough projectives and enough injectives. We define a proper $m$-term subcategory $\mathcal G$ on $\mathcal B$, which is an extriangulated subcategory. Then we give a correspondence…

In the category of finitely generated modules over an artinian ring, we classify all the abelian exact subcategories closed under predecessors or, equivalently, all the split torsion pairs with torsion-free class closed under quotients.

Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let $\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP} gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and the number of…

For a left artinian ring A, we study the lattice torsA of torsion pairs in the category of finitely generated A-modules by considering an isomorphic lattice formed by certain closed sets in a topological space associated to A, the Ziegler…

Following arguments that the (hidden) M-algebra serves as the maximal super-exceptional tangent space for 11D supergravity, we make explicit here its integration to a (super-Lie) group. This is equipped with a left-invariant extension of…

In this paper, we first give a characterization of silting objects in the comma category Assume that C1 and C2 are two subcategories of left R-modules, D1 and D2 be two subcategories of left S-modules. We mainly prove that (C1, C2) and (D1,…

Let $T$ be a monad on a category $\mathscr{C}$. In this paper, we introduce the notion of higher derivations on the monad $T$ and characterize them in terms of ordinary derivations on $T$. We also define higher derivations on modules over…

We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…

In this paper we introduce $n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories by axiomatising properties of $n\mathbb{Z}$-cluster tilting subcategories. We study this categories and show that every $n\mathbb{Z}$-cluster tilting…

We show that every higher Auslander algebra $A_{n+1}^d$ of type $\mathbb{A}$ such that $\gcd(n,d)=1$ is derived equivalent to a certain replicated algebra $B=B_0^{(n+d)}$. Moreover ${\rm{gldim}} B = nd$ and $B$ admits an $nd$-cluster…

The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By…

In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then torsion pairs in $\mathcal A$ and $\mathcal C$ can induce torsion pairs in $\mathcal B$, and the converse holds…

Let A be an abelian variety defined over a number field K, the number of torsion points rational over a finite extension L is bounded polynomially in terms of the degree [L : K]. When A is isogenous to a product of simple abelian varieties…

The notion of a pseudo cluster tilting subcategory $\mathcal X$ in an extriangulated category $\mathcal C$ is defined in this article. We prove that the quotient category $\mathcal C/\mathcal X$, obtained by factoring an extriangulated…