Author:
Pardo-Guerra Sebastián,Rincón-Mejía Hugo A.,Zorrilla-Noriega Manuel G.,González-Bayona Francisco
Abstract
AbstractThe collection of all cohereditary classes of modules over a ring R is a pseudocomplemented complete big lattice. The elements of its skeleton are the conatural classes of R-modules. In this paper we extend some results about cohereditary classes in R-Mod to the category $$\mathcal {L_{M}}$$
L
M
of linear modular lattices, which has as objects all complete modular lattices and as morphisms all linear morphisms. We introduce the big lattice of conatural classes in $$\mathcal {L_{M}}$$
L
M
, and we obtain some results about it, paralleling the case of R-Mod and arriving at its being boolean. Finally, we prove some closure properties of conatural classes in $$\mathcal {L_{M}}$$
L
M
.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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