Density Relative to a Torsion Theory
Copyright policy )Density Relative to a Torsion Theory
If ( ℑ , F ) (\Im , \mathcal {F}) is a torsion theory on Mod R R , then a ring B B of biendomorphisms of a ℑ \Im -cocritical module is topologized. Moreover, if a certain factor module of R R is quasi-projective, a ring monomorphism φ : R → B \varphi :R \to B is found such that φ ( R ) \varphi (R) is topologically dense in B B . This is done in such a way that when ( ℑ , F ) (\Im , \mathcal {F}) is the torsion theory in which every module is torsion free, the Jacobson density theorem is recovered.
biendomorphisms, cocritical module, Jacobson density theorem, Free, projective, and flat modules and ideals in associative algebras, Torsion theories; radicals on module categories (associative algebraic aspects), Simple and semisimple modules, primitive rings and ideals in associative algebras
biendomorphisms, cocritical module, Jacobson density theorem, Free, projective, and flat modules and ideals in associative algebras, Torsion theories; radicals on module categories (associative algebraic aspects), Simple and semisimple modules, primitive rings and ideals in associative algebras
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