On the lattice of conatural classes of linear modular lattices

被引:0
|
作者
Pardo-Guerra, Sebastian [1 ]
Rincon-Mejia, Hugo A. [2 ]
Zorrilla-Noriega, Manuel G. [2 ]
Gonzalez-Bayona, Francisco [2 ]
机构
[1] Univ Calif San Diego, Dept Bioengn, San Diego, CA USA
[2] Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Ciudad de Mexico, Mexico
关键词
Big lattices; Modular lattices; Linear morphism of lattices; Cohereditary classes; Conatural classes;
D O I
10.1007/s00012-023-00828-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The 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 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 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 L-M.
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页数:18
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