Related papers: Separated presentations of modules over pullback r…
We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded…
We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
In this article, we present the basic definitions of modules and Lie semialgebras over semirings with a negation map. Our main example of a semiring with a negation map is ELT algebras, and some of the results in this article are formulated…
Let R be a ring of polynomials in a finite number of variables over a perfect field k of characteristic p>0 and let F:R\to R be the Frobenius map of R, i.e. F(r)=r^p. We explicitly describe an R-module isomorphism Hom_R(F_*(M),N)\cong…
The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…
We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and morphisms of finite Tor-dimension, respectively. The class of…
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
Basic modules of McLain groups $M=M(\Lambda,\leq, R)$ are defined and investigated. These are (possibly infinite dimensional) analogues of Andr\'e's supercharacters of $U_n(q)$. The ring $R$ need not be finite or commutative and the field…
Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…
In this short note, we construct a right adjoint to the functor which associates to a ring $R$ equipped with a group action its twisted group ring. This right adjoint admits an interpretation as semilinearization, in that it sends an…
Given a good $n$-tilting module $T$ over a ring $A$, let $B$ be the endomorphism ring of $T$, it is an open question whether the kernel of the left-derived functor $T\otimes^L_B-$ between the derived module categories of $B$ and $A$ could…
P. M. Cohn showed in 1971 that given a ring $R$, to describe, up to isomorphism, a division ring $D$ generated by a homomorphic image of $R$ is equivalent to specifying the set of square matrices over $R$ which map to singular matrices over…
Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…
By any measure, semisimple modules form one of the most important classes of modules and play a distinguished role in the module theory and its applications. One of the most fundamental results in this area is the Wedderburn-Artin theorem.…
Associated to a Thurston map $f: S^2 \to S^2$ with postcritical set $P$ are several different invariants obtained via pullback: a relation on the set of free homotopy classes of curves in $S^2- P$, a linear operator on the free $\R$-module…
World models have been recently proposed as sandbox environments in which AI agents can be trained and evaluated before deployment. While realistic world models often have high computational demands, this can often be alleviated by…
An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. The group ring $RG$ of a finite group $G$ is isomorphic to the set of {\em group ring matrices} over $R$. It is shown that…
This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…
A $\mathbb{Z}^d$-graded differential $R$-module is a $\mathbb{Z}^d$-graded $R$-module $D$ equipped with an endomorphism, $\delta$, that squares to zero. For $R=k[x_1,\ldots,x_d]$, this paper establishes a lower bound on the rank of such a…