Geodesic
$n$-strongly Gorenstein graded modules
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 55-73 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $R$ be a graded ring and $n\geq 1$ 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.
Let $R$ be a graded ring and $n\geq 1$ 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.
DOI : 10.21136/CMJ.2018.0160-17
Classification : 16E05, 16W50, 18G25
Keywords: $n$-strongly Gorenstein gr-injective module; $n$-strongly Gorenstein gr-flat module; $n$-strongly Gorenstein gr-projective module 
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Gao, Zenghui; Peng, Jie. $n$-strongly Gorenstein graded modules. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 55-73. doi: 10.21136/CMJ.2018.0160-17

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