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Lattice decomposition of modules
dc.contributor.author | García Hernández, Josefa María | |
dc.contributor.author | Jara Martínez, Pascual | |
dc.contributor.author | Merino González, Luis Miguel | |
dc.date.accessioned | 2021-09-16T12:12:48Z | |
dc.date.available | 2021-09-16T12:12:48Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | García, J. M., Jara, P., & Merino, L. M. (2021). Lattice decomposition of modules. International Electronic Journal of Algebra Volume 30 (2021) 285-303. DOI: [10.24330/ieja.969940] | es_ES |
dc.identifier.uri | http://hdl.handle.net/10481/70239 | |
dc.description.abstract | The first aim of this work is to characterize when the lattice of all submodules of a module is a direct product of two lattices. In particular, which decompositions of a module M produce these decompositions: the lattice decompositions. In a first etage this can be done using endomorphisms of M, which produce a decomposition of the ring EndR(M) as a product of rings, i.e., they are central idempotent endomorphisms. But since not every central idempotent endomorphism produces a lattice decomposition, the classical theory is not of application. In a second step we characterize when a particular module M has a lattice decomposition; this can be done, in the commutative case in a simple way using the support, Supp(M), of M; but, in general, it is not so easy. Once we know when a module decomposes, we look for characterizing its decompositions. We show that a good framework for this study, and its generalizations, could be provided by the category sigma[M], the smallest Grothendieck subcategory of Mod - R containing M. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | International Electronic Journal of Algebra | es_ES |
dc.rights | Atribución 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject | Module | es_ES |
dc.subject | Ring | es_ES |
dc.subject | Lattice | es_ES |
dc.subject | Lattice decomposition | es_ES |
dc.subject | Grothendieck category | es_ES |
dc.title | Lattice decomposition of modules | es_ES |
dc.type | journal article | es_ES |
dc.rights.accessRights | open access | es_ES |
dc.identifier.doi | 10.24330/ieja.969940 | |
dc.type.hasVersion | VoR | es_ES |