Relative weak derived functors

Panneerselvam Prabakaran

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 1, page 35-50
  • ISSN: 0010-2628

Abstract

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Let R be a ring, n a fixed non-negative integer, 𝒲 ℐ the class of all left R -modules with weak injective dimension at most n , and 𝒲 ℱ the class of all right R -modules with weak flat dimension at most n . Using left (right) 𝒲 ℐ -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that - ⊗ - is right balanced on ℳ R × R ℳ by 𝒲 ℱ × 𝒲 ℐ , and investigate the global right 𝒲 ℐ -dimension of R ℳ by right derived functors of ⊗ .

How to cite

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Prabakaran, Panneerselvam. "Relative weak derived functors." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 35-50. <http://eudml.org/doc/297191>.

@article{Prabakaran2020,
abstract = {Let $R$ be a ring, $n$ a fixed non-negative integer, $\{\mathcal \{W I\}\}$ the class of all left $R$-modules with weak injective dimension at most $n$, and $\{\mathcal \{W F\}\}$ the class of all right $R$-modules with weak flat dimension at most $n$. Using left (right) $\{\mathcal \{W I\}\}$-resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that $- \otimes -$ is right balanced on $\{\mathcal \{M\}\}_R \times \{_R\{\mathcal \{M\}\}\}$ by $\{\mathcal \{W F\}\} \times \{\mathcal \{W I\}\}$, and investigate the global right $\{\mathcal \{W I\}\}$-dimension of $_R\{\mathcal \{M\}\}$ by right derived functors of $\otimes $.},
author = {Prabakaran, Panneerselvam},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weak injective module; weak flat module; weak injective dimension; weak flat dimension},
language = {eng},
number = {1},
pages = {35-50},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relative weak derived functors},
url = {http://eudml.org/doc/297191},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Prabakaran, Panneerselvam
TI - Relative weak derived functors
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 35
EP - 50
AB - Let $R$ be a ring, $n$ a fixed non-negative integer, ${\mathcal {W I}}$ the class of all left $R$-modules with weak injective dimension at most $n$, and ${\mathcal {W F}}$ the class of all right $R$-modules with weak flat dimension at most $n$. Using left (right) ${\mathcal {W I}}$-resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that $- \otimes -$ is right balanced on ${\mathcal {M}}_R \times {_R{\mathcal {M}}}$ by ${\mathcal {W F}} \times {\mathcal {W I}}$, and investigate the global right ${\mathcal {W I}}$-dimension of $_R{\mathcal {M}}$ by right derived functors of $\otimes $.
LA - eng
KW - weak injective module; weak flat module; weak injective dimension; weak flat dimension
UR - http://eudml.org/doc/297191
ER -

References

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