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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (10): 14-16.doi: 10.6040/j.issn.1671-9352.0.2017.654

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Gorenstein代数上的倾斜模的个数

陈文倩,张孝金*,昝立博   

  1. 南京信息工程大学数学与统计学院, 江苏 南京 210044
  • 收稿日期:2017-12-28 出版日期:2018-10-20 发布日期:2018-10-09
  • 作者简介:陈文倩(1994— )女,硕士研究生,研究方向为代数表示论. E-mail:chenwenqianaa@163.com*通信作者简介:张孝金(1983— )男, 博士,副教授, 研究方向为代数表示论. E-mail:xjzhang@nuist.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11571164,11671174);江苏省自然科学基金资助项目(BK20130983)

The number of tilting modules over Gorenstein algebras

CHEN Wen-qian, ZHANG Xiao-jin*, ZAN Li-bo   

  1. School of Mathematics and Statistics, Nanjing University of Information Science &
    Technology, Nanjing 210044, Jiangsu, China
  • Received:2017-12-28 Online:2018-10-20 Published:2018-10-09

摘要: A是一个Gorenstein代数,则倾斜右A-模的个数等于倾斜左A-模的个数。给出反例说明自内射维数大于等于2的Gorenstein代数B的经典倾斜右B-模的个数不一定等于经典倾斜左B-模的个数。

关键词: Gorenstein代数, 倾斜模, 余倾斜模

Abstract: For a Gorenstein algebra A, the number of tilting right A-modules is equal to the number of tilting left A-modules. A counter-example is given to show that for a Gorenstein algebra B with self-injective dimension no less than 2, the number of classical tilting left B-modules is not necessary to be equal to that of classical tilting right B-modules.

Key words: Gorenstein algebra, tilting module, cotilting module

中图分类号: 

  • O154.2
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