$f$-derivations on rings and modules

Bland, Paul E.. "$f$-derivations on rings and modules." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 379-390. <http://eudml.org/doc/249876>.

@article{Bland2006,
abstract = {If $\tau $ is a hereditary torsion theory on $\mathbf \{Mod\}_\{R\}$ and $Q_\{\tau \}:\mathbf \{Mod\}_\{R\}\rightarrow \mathbf \{Mod\}_\{R\}$ is the localization functor, then we show that every $f$-derivation $d:M\rightarrow N$ has a unique extension to an $f_\{\tau \}$-derivation $d_\{\tau \}:Q_\{\tau \}(M)\rightarrow Q_\{\tau \}(N)$ when $\tau $ is a differential torsion theory on $\mathbf \{Mod\}_\{R\}$. Dually, it is shown that if $\tau $ is cohereditary and $C_\{\tau \}:\mathbf \{Mod\}_\{R\}\rightarrow \mathbf \{Mod\}_\{R\}$ is the colocalization functor, then every $f$-derivation $d:M\rightarrow N$ can be lifted uniquely to an $f_\{\tau \}$-derivation $d_\{\tau \}:C_\{\tau \}(M)\rightarrow C_\{\tau \}(N)$.},
author = {Bland, Paul E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {torsion theory; differential filter; localization; colocalization; $f$-derivation; torsion theory; differential filter; localization; colocalization; -derivation},
language = {eng},
number = {3},
pages = {379-390},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$f$-derivations on rings and modules},
url = {http://eudml.org/doc/249876},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Bland, Paul E.
TI - $f$-derivations on rings and modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 379
EP - 390
AB - If $\tau $ is a hereditary torsion theory on $\mathbf {Mod}_{R}$ and $Q_{\tau }:\mathbf {Mod}_{R}\rightarrow \mathbf {Mod}_{R}$ is the localization functor, then we show that every $f$-derivation $d:M\rightarrow N$ has a unique extension to an $f_{\tau }$-derivation $d_{\tau }:Q_{\tau }(M)\rightarrow Q_{\tau }(N)$ when $\tau $ is a differential torsion theory on $\mathbf {Mod}_{R}$. Dually, it is shown that if $\tau $ is cohereditary and $C_{\tau }:\mathbf {Mod}_{R}\rightarrow \mathbf {Mod}_{R}$ is the colocalization functor, then every $f$-derivation $d:M\rightarrow N$ can be lifted uniquely to an $f_{\tau }$-derivation $d_{\tau }:C_{\tau }(M)\rightarrow C_{\tau }(N)$.
LA - eng
KW - torsion theory; differential filter; localization; colocalization; $f$-derivation; torsion theory; differential filter; localization; colocalization; -derivation
UR - http://eudml.org/doc/249876
ER -