Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Module Correspondences for Twisted Group Algebras

Abstract

Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K ^α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K ^α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K ^α G-modules and the set of irreducible K ^α C _G (A)-modules.     

Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability

Let Mn be the algebra of all n × n complex matrices and gl(n,C) be the general linear Lie algebra,where n ≥ 2.An invertible linear map ?:gl(n,C) →gl(n,C) preserves solvability in both directions if bot...     

The Almost Split Sequences for Trivial Extensions of Hereditary Algebras

Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.     

一道行列式证明题的多种证明方法

针对线性代数教材中一道行列式证明题，利用行列式的性质，给出多种证明方法，旨在启发学生对相关行列式计算或证明题的解题方法进行探索．     

完备化Witt代数中自然出现的一些非有限阶化李代数的表示

讨论了完备化Witt代数的三类非有限阶化子代数的不可约非权模的实现,并利用它们的表示得到一些有趣的组合恒等式.     

Second graders articulating ideas about linear functional relationships

In this paper, we explore the ideas that second grade students articulate about functional relationships. We adopt a function-based approach to introduce elementary school children to algebraic content. We present results from a design-based research study carried out with 21 second-grade students (approximately 7 years of age). We focus on a lesson from our classroom teaching experiment in which the students were working on a problem that involved a linear functional relationship (y = 2x). From the analysis of students’ written work and classroom video, we illustrate two different approaches that students adopt to express the relationship between two quantities. Students show fluency recontextualizing the problem posed, moving between extra-mathematical and intra-mathematical contexts.