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The Osofsky-Smith Theorem for Modular Lattices,and Applications (II) |
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| Authors: | Toma Albu |
| Institution: | 1. Simion Stoilow Institute of Mathematics of the Romanian Academy , Bucharest , Romania Toma.Albu@imar.ro |
| Abstract: | This is the second part of the paper with the same title published in Communications in Algebra in 2011. It contains applications of the Latticial Osofsky–Smith Theorem to Grothendieck categories and module categories equipped with a torsion theory. Various many different meanings spread in the literature of the relative concepts with respect to a hereditary torsion theory τ on Mod-R like τ-essential submodule, τ-complement submodule, τ-CS module, etc. are also discussed. |
| Keywords: | Finitely generated object Grothendieck category Locally finitely generated category The Categorical Osofsky-Smith Theorem The Latticial Osofsky-Smith Theorem The Relative Osofsky–Smith Theorem Torsion theory τ-CS module τ-Compact module τ-Compactly generated module τ-Finitely generated module |