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n - gr -coherent rings and Gorenstein graded modules

Mostafa Amini, Driss Bennis, Soumia Mamdouhi (2022)

Czechoslovak Mathematical Journal

Let R be a graded ring and n ≥ 1 be an integer. We introduce and study the notions of Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules by using the notion of special finitely presented graded modules. On n -gr-coherent rings, we investigate the relationships between Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules. Among other results, we prove that any graded module in R -gr (or gr- R ) admits a Gorenstein n -FP-gr-injective (or Gorenstein n -gr-flat) cover and preenvelope, respectively....

n -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

Let R be a graded ring and n ≥ 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...

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