试论卡普兰斯基的多项式恒等式环与正交模格思想  

On Irving Kaplansky’s Thought of Polynomial Identity Ring and Orthomodular Lattic

作　　者：杨中明 王淑红[1] YANG Zhongming;WANG Shuhong(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024

出　　处：《中国科技史杂志》2020年第2期156-165,共10页The Chinese Journal for the History of Science and Technology

基　　金：国家自然科学基金资助项目(项目编号:11871018)。

摘　　要：美国数学家卡普兰斯基主要研究代数学,在环论、模论、群论等代数领域做出了里程碑式的成果。本文通过文献考证和概念分析,重点对卡普兰斯基的两篇抽象代数学代表作进行研究。研究表明:他证明了一个具有多项式恒等式的本原代数在其中心上是有限维的,开创了非交换代数的重要分支;他在模格领域引入"正交"概念,首次将以正交偶为模对的正交补格命名为"正交模格",证明了任何正交补完备模格都是连续几何。American mathematician Irving Kaplansky is a famous algebraist.He had made landmark achievements in the fields of ring theory,module theory,group theory and so on.Through literature textual research and conceptual analysis,this paper has studied two representative works of abstract algebra of Kaplansky.The results are as follows.Kaplansky has proved that a primitive algebra with polynomial identity is of finite dimension over its center,and in doing so he has invented an important branch of non-commutative algebra.He has introduced the concept of"orthogonality"into the field of orthomodular lattice,named the orthogonal complement lattice with orthogonal pair as modular pair as"orthomodular lattice" for the first time,and proved that any orthocomplemented complete modular lattice is a continuous geometry.

关 键 词：卡普兰斯基 多项式恒等式 正交模格 连续几何 

分 类 号：N09[自然科学总论—科学技术哲学] O1-0[理学—数学]