@misc{10481/70239,
year = {2021},
url = {http://hdl.handle.net/10481/70239},
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.},
publisher = {International Electronic Journal of Algebra},
keywords = {Module},
keywords = {Ring},
keywords = {Lattice},
keywords = {Lattice decomposition},
keywords = {Grothendieck category},
title = {Lattice decomposition of modules},
doi = {10.24330/ieja.969940},
author = {García Hernández, Josefa María and Jara Martínez, Pascual and Merino González, Luis Miguel},
}