王淼,王占平.Frobenius扩张上的$n$-Gorenstein投射模和维数[J].数学研究及应用,2021,41(1):25~32
Frobenius扩张上的$n$-Gorenstein投射模和维数
$n$-Gorenstein Projective Modules and Dimensions over Frobenius Extensions
投稿时间:2020-02-16  修订日期:2020-09-26
DOI:10.3770/j.issn:2095-2651.2021.01.004
中文关键词:  Frobenius扩张  $n$-Gorenstein投射模  $n$-Gorenstein投射维数
英文关键词:Frobenius extensions  $n$-Gorenstein projective modules  $n$-Gorenstein projective dimensions
基金项目:国家自然科学基金(Grant No.11561061).
作者单位
王淼 西北师范大学数学系, 甘肃 兰州 730070 
王占平 西北师范大学数学系, 甘肃 兰州 730070 
摘要点击次数: 34
全文下载次数: 34
中文摘要:
      本文讨论了Frobenius扩张上的$n$-Gorenstein投射模和$n$-Gorenstein投射维数.设$R\subset A$是环的Frobenius扩张, $M$是任意左$A$-模. 证明了: $M$是$n$-Gorenstein投射左$A$-模当且仅当$A\otimes_{R}M$和$\mathrm{Hom}_{R}(A,M)$是$n$-Gorenstein投射左$A$-模当且仅当$M$是$n$-Gorenstein投射左$R$-模.进而,当$R\subset A$是可分Frobenius扩张时,考虑了$n$-Gorenstein投射维数.
英文摘要:
      In this paper, we study $n$-Gorenstein projective modules over Frobenius extensions and $n$-Gorenstein projective dimensions over separable Frobenius extensions. Let $R\subset A$ be a Frobenius extension of rings and $M$ any left $A$-module. It is proved that $M$ is an $n$-Gorenstein projective left $A$-module if and only if $A\otimes_{R}M$ and $\mathrm{Hom}_{R}(A,M)$ are $n$-Gorenstein projective left $A$-modules if and only if $M$ is an $n$-Gorenstein projective left $R$-module. Furthermore, when $R\subset A$ is a separable Frobenius extension, $n$-Gorenstein projective dimensions are considered.
查看全文  查看/发表评论  下载PDF阅读器