模余代数和Morita-Takeuchi关系

H是Hopf代数,C是H-模余代数。首先利用余积分的概念,诱导C的右H-余模结构,并构造了Smash余积余代数C×H,使C×H作为余代数同构于C H。然后,由C的右H-余模结构诱导C的左H0-模结构,令 C=C/KerεH0C,则C×H与 C有Morita-Takeuchi关系。     

Expanding conceptions of utility: middle school students’ perspectives on the usefulness of mathematics

This research explores how adolescents conceptualize the usefulness of mathematics. Integrating sociocultural theory with the study of utility value, this study uses open-ended survey items and interview tasks to examine conceptions of usefulness among a group of predominantly Latinx middle school students. Findings reveal that students primarily conceptualized the usefulness of mathematics in two ways. First, students considered the applicability of mathematics content, focusing on applications of mathematics in everyday life and future jobs/careers. Second, students considered the usefulness of features of the learning experience, such as the form of interaction and structure of the activity. Both conceptions are compared to existing conceptions of usefulness in the literature, and implications for classroom practice and future research are discussed.     

G-集分次模与Morita Context

对任意群Ｇ， Ｈ≤Ｇ，［１］研究了Ｇ－分次环Ｒ与有限可迁Ｇ－集的ｓｍａｓｈ积.在本文中我们对任意可迁Ｇ－集，讨论了一个关于Ｒ（Ｈ）与ｓｍａｓｈ积Ｒ＃Ｇ／Ｈ的Ｍｏｒｉｔａ ｃｏｎｔｅｘｔ，从而推广了［２］，［３］，［４］给出的关于Ｇ－分次环及其与群Ｇ的ｓｍａｓｈ积的一些重要结果．     

分布式系统的层次式命名方案设计

针对大规模分布式系统中对象迁移、网络和系统动态重构的要求,本文提出了一种层次式的命名和编址方案,它将对位置透明的标识（ＯＩＤ）和表示位置的地址（ＯＡＤ）二者结合起来标识对象．     

Stable Ranges For Morita Contexts

In this paper, we show that if rings A and B are (s, 2)-rings, then so is the ring of a Morita context (A, B, M, N, , ). Also we get analogous results for unit 1-stable ranges and GM-rings. These give new classes of rings satisfying such stable range conditions.2000 Mathematics Subject Classification: 16U99 16E50     

The semantics of knowledge attributions

The basic idea of conversational contextualism is that knowledge attributions are context sensitive in that a given knowledge attribution may be true if made in one context but false if made in another, owing to differences in the attributors’ conversational contexts. Moreover, the context sensitivity involved is traced back to the context sensitivity of the word “know,” which, in turn, is commonly modelled on the case either of genuine indexicals such as “I” or “here” or of comparative adjectives such as “tall” or “rich.” But contextualism faces various problems. I argue that in order to solve these problems we need to look for another account of the context sensitivity involved in knowledge attributions and I sketch an alternative proposal.     

森田六元组的几乎分裂序列

令ΛA_1,Λ_2为两个环,M是(A_2-Λ_1)-双模,且N是(Λ_1-Λ_2)-双模.六元组Γ=(Λ_1,Λ_2,N,M,ψ,φ)是一个森田六元组.对于Γ的表示,确定其几乎分裂序列(也称AR-序列)是非常重要的.通过modΛ_1和modΛ_2的右(左)几乎分裂同态、既约同态构造Γ上的相应同态,并进一步确定它的几乎分裂序列.     

Hopf代数胚上的Smash积的Maschke型定理和Morita关系

本文研究了Hopf代数胚上的Smash积代数.利用Hopf代数胚的积分理论,获得了Hopf代数胚上的Smash的Maschke型定理并构造了一个Morita关系,推广了Cohen和Fishman在文献[1]中的相应结果.作为应用,获得了Hopf代数胚上的余模代数的Maschke型定理.     

On computable formal concepts in computable formal contexts

We introduce and study the notions of computable formal context and computable formal concept. We give some examples of computable formal contexts in which the computable formal concepts fail to form a lattice and study the complexity aspects of formal concepts in computable contexts. In particular, we give some sufficient conditions under which the computability or noncomputability of a formal concept could be recognized from its lattice-theoretic properties. We prove the density theorem showing that in a Cantor-like topology every formal concept can be approximated by computable ones. We also show that not all formal concepts have lattice-theoretic approximations as suprema or infima of families of computable formal concepts.