Related papers: Idempotent ideals and the Igusa-Todorov functions

Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts…

We define the completion of an associative algebra $A$ in a set $M=\{M_1,\dots,M_r\}$ of $r$ right $A$-modules in such a way that if $\mathfrak a\subseteq A$ is an ideal in a commutative ring $A$ the completion $A$ in the (right) module…

In this paper we study the lower triangular matrix $\mathbb{K}$-algebra $\Lambda:=\left[\begin{smallmatrix} T & 0 \\ M & U \end{smallmatrix}\right],$ where $U$ and $T$ are basic $\mathbb{K}$-algebras with enough idempotents and $M$ is an…

Let $\Lambda$ be an artin algebra and let $\mathcal{P}^{<\infty}_\Lambda$ the category of finitely generated right $\Lambda$-modules of finite projective dimension. We show that $\mathcal{P}^{<\infty}_\Lambda$ is contravariantly finite in…

In the first part of this paper we present explicit formulas for primitive idempotents in arbitrary Frobenius algebras using the entries of representing matrices coming from projective indecomposable modules with respect to a certain choice…

We interpolate cohomology classes attached to families of Hilbert modular forms. Using this we construct a two variable $p$-adic L-function which interpolates one variable $p$-adic L-functions.

For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive…

For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $\Lambda$ is constructed, with the property that $\text{fin.dim}_n\, \Lambda =…

Let $R$ be a discrete valuation domain with field of fractions $Q$ and maximal ideal generated by $\pi$. Let $\Lambda$ be an $R$-order such that $Q\Lambda$ is a separable $Q$-algebra. Maranda showed that there exists $k\in\mathbb{N}$ such…

We construct \Lambda-adic de Rham and crystalline analogues of Hida's ordinary \Lambda-adic etale cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic extension of \Q_p, we prove appropriate…

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…

We study stratifying ideals for rings in the context of relative homological algebra. Using LU-decompositions, which are a special type of twisted products, we give a sufficient condition for an idempotent ideal to be (relative)…

In this paper we continue the study of edge-colored graphs associated with finite idempotent algebras initiated in arXiv:2006.09599. We prove stronger connectivity properties of such graphs that will allows us to demonstrate several useful…

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are…

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…

For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and `real harmonic functions' with respect to A. We also consider certain groups…

The aim of this paper is to unify classification theories of torsion classes of finite dimensional algebras and commutative Noetherian rings. For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $\Lambda$, we study the set…

Let $\Lambda$ be a commutative local uniserial ring of length at least seven with radical factor ring $k$. We consider the category $S(\Lambda)$ of all possible embeddings of submodules of finitely generated $\Lambda$-modules and show that…

Using combinatorics of Young tableaux, we give an explicit construction of irreducible graded modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\lambda}$ of type $A_{n}$. Our construction is compatible…

Let R be a (unital) commutative ring, and G be a finite group with order invertible in R. We introduce new idempotents in the double Burnside algebra RB(G,G), indexed by conjugacy classes of minimal sections of G, i.e. pairs (T,S) of…