n -strongly Gorenstein graded modules

Zenghui Gao; Jie Peng

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 55-73
  • ISSN: 0011-4642

Abstract

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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 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.

How to cite

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Gao, Zenghui, and Peng, Jie. "$n$-strongly Gorenstein graded modules." Czechoslovak Mathematical Journal 69.1 (2019): 55-73. <http://eudml.org/doc/294148>.

@article{Gao2019,
abstract = {Let $R$ be a graded ring and $n\ge 1$ 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.},
author = {Gao, Zenghui, Peng, Jie},
journal = {Czechoslovak Mathematical Journal},
keywords = {$n$-strongly Gorenstein gr-injective module; $n$-strongly Gorenstein gr-flat module; $n$-strongly Gorenstein gr-projective module},
language = {eng},
number = {1},
pages = {55-73},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$n$-strongly Gorenstein graded modules},
url = {http://eudml.org/doc/294148},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Gao, Zenghui
AU - Peng, Jie
TI - $n$-strongly Gorenstein graded modules
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 55
EP - 73
AB - Let $R$ be a graded ring and $n\ge 1$ 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.
LA - eng
KW - $n$-strongly Gorenstein gr-injective module; $n$-strongly Gorenstein gr-flat module; $n$-strongly Gorenstein gr-projective module
UR - http://eudml.org/doc/294148
ER -

References

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