Related papers: On a $\mathbb{Z}$-module connected to approximatio…

In this paper we use A-infinity modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A-infinity modules. These varieties carry an action of an algebraic…

We introduce to the context of multigraded modules the methods of modules over categories from algebraic topology and homotopy theory. We develop the basic theory quite generally, with a view toward future applications to a wide class of…

To a given Pisot unit $\beta$ we associate a finite abelian group whose size appears to be equal to the discriminant of $\beta$. We call it the Pisot group and find its representation in the two-sided $\beta$-compactum in the case of…

We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the chains of homomorphisms $M_0 \stackrel{f_1}{\rightarrow} M_1…

A finite abelian $p$-group having an automorphism $x$ such that $1+\ldots+x^{p-1}=0$, can be viewed as a module over an appropriate discrete valuation ring $\mathcal{O}$ containing $\mathbb{Z}_p$ (the ring of $p$-adic integer). This yields…

Let $p$ be a prime number. By a result of Ozaki, the capitulations of ideals in ${\Bbb Z}_p$-extensions and the finite submodules of Iwasawa modules are closely related. In this article, we discuss this relationship in ${\Bbb…

Fix a poset $P$ and a natural number $n$. For various commutative local rings $\Lambda$, each of Loewy length $n$, consider the category $\textrm{sub}_\Lambda P$ of $\Lambda$-linear submodule representations of $P$. We give a criterion for…

Let $K$ be a field of characteristic $p>0$, $A=K[[Y]]$ be a power series ring in one variable and $Q(A)$ be the field of fraction of $A$. Suppose that $R=A[X_1,\ldots,X_n]$ is a standard $\mathbb{N}^n$-graded polynomial ring over $A$, i.e.,…

Let $k$ be a field and let $E$ be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra $L_k (E)$ and show its close relationship with the finite-dimensional representations…

We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, even over $\mathbb Z,$ and study connections…

We generalize the work of Ohta on the congruence modules attached to elliptic Eisenstein series to the setting of Hilbert modular forms. Our work involves three parts. In the first part, we construct Eisenstein series adelically and compute…

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence…

This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number $\alpha$ such that $\Q[\alpha] = \F$ given a real Galois extension $\F$ of $\Q$ by its integral…

In this paper we develop a general theory of modules which are invariant under automorphisms of their covers and envelopes. When applied to specific cases like injective envelopes, pure-injective envelopes, cotorsion envelopes, projective…

Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very…

Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N; M), on Specs(M) equipped with the dual Zariski topology…

Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

We study the interplay between the notions of $n$-coherent rings and finitely $n$-presented modules, and also study the relative homological algebra associated to them. We show that the $n$-coherency of a ring is equivalent to the thickness…

Let H be a Hopf algebra with bijective antipode, let \alpha, \beta be two Hopf algebra automorphisms of H and M a finite dimensional (\alpha, \beta )-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an…

In this paper we determine the topology of the moduli space $\mathcal{MS}_{1,1}(\vartheta)$ of surfaces of genus one with a Riemannian metric of constant curvature $1$ and one conical point of angle $2\pi\vartheta$. In particular, for…