Topics in noncommutative ring theory

非交换环理论主题

• 批准号: 194196-2010
• 负责人: Zhou, Yiqiang
• 金额: $ 0.87万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=476613
• 关键词: Topics; noncommutative; ring; theory

Modern algebra is generally considered as the universal language of natural sciences. Ring theory has become an important part of modern algebra because of its increasing significance to other branches of mathematics, computer science and physics. The aim here is to continue the applicant's investigations of rings, which are sets in which one can ``add'' and ``multiply'' with the usual rules of distributivity connecting these two operations. The classical examples are the ring of integers with the usual operations, the ring of all polynomials with integer or rational coefficients, and the ring of n by n matrices whose entries are real numbers.

现代代数通常被认为是自然科学的通用语言。环理论已成为现代代数的重要组成部分，因为它对数学、计算机科学和物理学的其他分支的重要性日益增加。 这里的目的是继续申请人对环的研究，在环中可以使用连接这两个运算的通常分配规则进行“加法”和“乘法”。经典的例子是整数环与通常的操作，环的所有多项式与整数或合理的系数，和环的n乘n矩阵的条目是真实的数字。