contact us

Degenerations for Modules Over Representation-Finite Algebras

Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1313-1322

Author :

Abstract : Let A be a representation-finite algebra. We show that a finite dimensional A-module M degenerates to another A-module N if and only if the inequalities dim $_{K}$ Hom $_{A}$ (M, X) $\leq $ dim $_{K}$ Hom $_{A}$ (N, X) hold for all A-modules X. We prove also that if Ext $_{A}^{1}$ (X, X) = 0 for any indecomposable A-module X, then any degeneration of A-modules is given by a chain of short exact sequences.

Keyword : Primary 14L30, 16G60, 16G70

On Covering Multiplicity

Let A = {a $_{s}$ + n $_{s}{\Bbb Z}$ } $_{s=1}^{k}$ be a system of arithmetic sequences..

A Simple Proof of a Curious Congruence by Sun

In this note, we give a simple and elementary proof of the following curious congruence which..

Representing Quasi-Orders by Embeddability Ordering of Families of Topological ..

An elementary argument constructs, for each cardinal $\alpha $ , a topological space whose ..

On Swan Conductors for Brauer Groups of Curves Over Local Fields

For an element w of the Brauer group of a curve over a local field, we define the Swan conduc..

The Ideal of Polynomials Vanishing on a Commutative Ring

We determine equivalent conditions on a commutative Artinian ring S in order that the ideal o..

Conical Limit Set and Poincare Exponent for Iterations of Rational Functions

We contribute to the dictionary between action of Kleinian groups and iteration of rational f..

A Gauss-Kusmin Theorem for Optimal Continued Fractions

A Gauss-Kusmin theorem for the Optimal Continued Fraction (OCF) expansion is obtained. In ord..

Local Tomography with Nonsmooth Attenuation

Local tomography for the Radon transform with nonsmooth attenuation is proposed and justified..

Simple Families of Thue Inequalities

We use the hypergeometric method to solve three families of Thue inequalities of degree 3, 4 ..

Criteria of Algebraic Independence with Multiplicities and Interpolation Determ..

We generalize Gelfonds criterion of algebraic independence by taking into account the values ..