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

来源：

ALGEBRA UNIVERSALIS | 2023年 / 84卷 / 04期

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.

引用

页数：18

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