Related papers: Finite Modules over $\Bbb Z[t,t^{-1}]$

We calculate the number of the isomorphism class of the finite flat models over the ring of integers of an absolutely ramified $p$-adic field of constant group schemes of rank two over finite fields, by counting the rational points of a…

We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module $M$ over the Laurent polynomial ring $\Lambda_{\mu}=\mathbb{Z}[t_1^{\pm1},\dots,t_{\mu}^{\pm1}]$. If $D$ is a diagram of a…

Let $\Lambda$ be an artin algebra, and $\mathcal{V}$ a subset of all simple modules in $\mod\Lambda$. Suppose that $\Lambda/\rad \Lambda$ has finite syzygy type, then the derived dimension of $\Lambda$ is at most…

We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that…

A famous result due to L. S. Levy provides a classification of all finitely generated indecomposable modules over Dedekind-like rings. This motivates us to outline an approach to the classification of indecomposable pseudo-absorbing primary…

Let $R$ be an affine algebra over an algebraically closed field of characteristic $0$ with dim$(R)=n$. Let $P$ be a projective $A=R[T_1,\cdots,T_k]$-module of rank $n$ with determinant $L$. Suppose $I$ is an ideal of $A$ of height $n$ such…

Let $p$ be a fixed prime. We show that the number of isomorphism classes of finite rings of order $p^n$ is $p^\alpha$, where $\alpha=\frac{4}{27}n^3+O(n^{5/2})$. This result was stated (with a weaker error term) by Kruse and Price in 1969;…

Let W_n(K) be the Lie algebra of derivations of the polynomial algebra K[X]:=K[x_1,...,x_n] over an algebraically closed field K of characteristic zero. A subalgebra L of W_n(K) is called polynomial if it is a submodule of the K[X]-module…

Let $H$ be a generalized Liu algebra over an algebraically closed field $k$ of characteristic zero. We prove that all simple Yetter-Drinfeld modules over $H$ are finite-dimensional and present an explicit classification of these modules.…

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…

In this paper we establish lower and upper bounds for the cardinality of the profinite genus of the fundamental group $\pi_{1}(M_A)\cong (\mathbb{Z} \times \mathbb{Z})\rtimes_{A}\mathbb{Z}$ of a torus bundle $M_{A}$ in terms of the number…

Let KG be a group algebra of a finite p-group G over a finite field K of characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

Over a commutative local Cohen--Macaulay ring, we view and study the category of maximal Cohen--Macaulay modules as a ring with several objects. We compute the global dimension of this category and thereby extend a result of Leuschke to the…

Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the…

Let $G$ be a finitely generated abelian-by-finite group and $k$ a field of characteristic $p\ge 0$. The Euler class $[k_G]$ of $G$ over $k$ is the class of the trivial $kG$-module in the Grothendieck group $G_0(kG)$. We show that $[k_G]$…

There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\alpha}$, where $\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the…

We develop criteria for deciding the contravariant finiteness status of a subcategory $A \subseteq \Lambda\text{-mod}$, where $\Lambda$ is a finite dimensional algebra. In particular, given a finite dimensional $\Lambda$-module $X$, we…

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…