Mathematical Sciences: Problems in Universal Algebra

数学科学：泛代数问题

• 批准号: 8701643
• 负责人: Clifford Bergman
• 金额: $ 2.71万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701643&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Universal; Algebra

Three important properties of universal algebras will be studied: the amalgamation property, deductiveness, and congruence modular varieties. The research on the amalgamation property centers on two problems. 1. Determination if the amalgamation property plus residual smallness implies the congruence extension property. 2. Characterization of the amalgamation bases of the variety. The plans for deductiveness are less specific. The general issue is to attempt to classify those varieties that are deductive. A third avenue to be pursued is the representation problem for the commutator in congruence modular varieties. All of these topics concern the foundations of algebra and are likely to be applied outside of algebra only to the extent that they condition a mode of thought about algebraic questions.

泛代数的三个重要性质是 研究：合并属性，演绎性， 全等模变种 对合并财产的研究主要集中在两个方面 问题 1. 确定合并财产加上剩余财产 小意味着同余扩张性质。 2. 品种融合基础的表征。 演绎法的计划没有那么具体。 总 问题是试图对那些 演绎推理 第三个途径是代表权问题 在同余模簇中的换位子。 所有这些主题都涉及代数的基础， 很可能在代数之外被应用， 它们决定了代数问题的思维模式。