Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 55-73, 2019
$n$-strongly Gorenstein graded modules
Zenghui Gao, Jie Peng
Received April 3, 2017. Published online May 21, 2018.
Abstract: Let $R$ be a graded ring and $n\geq1$ an integer. We introduce and study $n$-strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that $n$-strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be $m$-strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever $n>m$. Many properties of the $n$-strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate the relations between the graded and the ungraded $n$-strongly Gorenstein injective (or flat) modules. In addition, the connections between the $n$-strongly Gorenstein gr-projective, gr-injective and gr-flat modules are considered.
Affiliations: Zenghui Gao, Jie Peng, College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan Province, P. R. China, e-mail: gaozenghui@cuit.edu.cn, pengjiecuit@163.com;