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单位积决定的若当矩阵代数（英文）
  • ISSN号：0255-7797
  • 期刊名称：《数学杂志》
  • 时间：0
  • 分类：O151.2[理学—数学;理学—基础数学]
  • 作者机构：[1]中国矿业大学理学院,江苏徐州221116
  • 相关基金：Supported by the Fundamental Research Fhnds for the Central Universities （2010LKSX05）; the National Natural Science Foundation of China （11171343）.
作者： 葛徽[1], 李小微[1]
关键词： 双线性映射, 零积决定的代数, 单位积决定的代数, bilinear maps, zero product determined algebras, identity product determinedalgebras
中文摘要：

本文研究了单位积决定的若当矩阵代数M=Mn（R）的条件及分类问题.利用基矩阵及巧妙对对称双线性映射{·,·}进行构造和扩充,用初等矩阵的方法,获得了一系列新的同样重要的定义,结论与证明（与参考文献[1]相比较）,推广了参考文献[1]的结论,作为其应用可以进一步证明了Mn（R）上的任意可逆线性映射都是保单位积的.

英文摘要：

In this paper, we investigate the condition and classification of the identity product determined Jordan matrix algebras M = Mn（R）. Using the base matrix and the symmetric bilinear map {.,.} skillfully constructed for this purpose and expansion, only elementary matrix method is used. Comparing to the reference [1], we obtain a new series of equally important definition, conclusions and proof improving the conclusions of the reference [1]. As an application we characterize the invertible linear maps on A/I which preserve identity （Jordan） product.

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期刊信息
  • 《数学杂志》
  • 北大核心期刊（2011版）
  • 主管单位:中华人民共和国教育部
  • 主办单位:武汉大学 湖北省数学学会 武汉数学学会
  • 主编：陈化
  • 地址：湖北武汉大学
  • 邮编：430072
  • 邮箱：jmath@whu.edu.cn
  • 电话：027-68754687
  • 国际标准刊号：ISSN：0255-7797
  • 国内统一刊号：ISSN：42-1163/O1
  • 邮发代号:38-71
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3910