Strongly 𝒲 -Gorenstein modules

Husheng Qiao; Zongyang Xie

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 441-449
  • ISSN: 0011-4642

Abstract

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Let 𝒲 be a self-orthogonal class of left R -modules. We introduce a class of modules, which is called strongly 𝒲 -Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly 𝒲 -Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly 𝒲 -Gorenstein module can be inherited by its submodules and quotient modules. As applications, many known results are generalized.

How to cite

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Qiao, Husheng, and Xie, Zongyang. "Strongly $\mathcal {W}$-Gorenstein modules." Czechoslovak Mathematical Journal 63.2 (2013): 441-449. <http://eudml.org/doc/260714>.

@article{Qiao2013,
abstract = {Let $\mathcal \{W\}$ be a self-orthogonal class of left $R$-modules. We introduce a class of modules, which is called strongly $\mathcal \{W\}$-Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly $\mathcal \{W\}$-Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly $\mathcal \{W\}$-Gorenstein module can be inherited by its submodules and quotient modules. As applications, many known results are generalized.},
author = {Qiao, Husheng, Xie, Zongyang},
journal = {Czechoslovak Mathematical Journal},
keywords = {self-orthogonal class; strongly $\mathcal \{W\}$-Gorenstein module; $\mathcal \{C\}$-resolution; self-orthogonal classes of modules; Gorenstein modules; resolutions},
language = {eng},
number = {2},
pages = {441-449},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strongly $\mathcal \{W\}$-Gorenstein modules},
url = {http://eudml.org/doc/260714},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Qiao, Husheng
AU - Xie, Zongyang
TI - Strongly $\mathcal {W}$-Gorenstein modules
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 441
EP - 449
AB - Let $\mathcal {W}$ be a self-orthogonal class of left $R$-modules. We introduce a class of modules, which is called strongly $\mathcal {W}$-Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly $\mathcal {W}$-Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly $\mathcal {W}$-Gorenstein module can be inherited by its submodules and quotient modules. As applications, many known results are generalized.
LA - eng
KW - self-orthogonal class; strongly $\mathcal {W}$-Gorenstein module; $\mathcal {C}$-resolution; self-orthogonal classes of modules; Gorenstein modules; resolutions
UR - http://eudml.org/doc/260714
ER -

References

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