Geodesic
Relative weak derived functors
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 35-50.

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Let $R$ be a ring, $n$ a fixed non-negative integer, ${\mathscr{W I}}$ the class of all left $R$-modules with weak injective dimension at most $n$, and ${\mathscr{W F}}$ the class of all right $R$-modules with weak flat dimension at most $n$. Using left (right) ${\mathscr{W I}}$-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 ${\mathscr{M}}_R \times {_R{\mathscr{M}}}$ by ${\mathscr{W F}} \times {\mathscr{W I}}$, and investigate the global right ${\mathscr{W I}}$-dimension of $_R{\mathscr{M}}$ by right derived functors of $\otimes$.
DOI : 10.14712/1213-7243.2020.015
Classification : 16E10, 16E30, 18G25
Keywords: weak injective module; weak flat module; weak injective dimension; weak flat dimension 
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Prabakaran, Panneerselvam. Relative weak derived functors. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 35-50. doi : 10.14712/1213-7243.2020.015. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.015/

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