Geodesic
Atoms in lattice of radical classes of lattice-ordered groups
Archivum mathematicum, Tome 29 (1993) no. 3-4, pp. 221-226 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a $K$-radical class is closed under taking $K$-isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices has a cover.
There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a $K$-radical class is closed under taking $K$-isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices has a cover.
Classification : 06F15
Keywords: lattice-ordered group; radical class; closure operator; atom 
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     title = {Atoms in lattice of radical classes of lattice-ordered groups},
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Ton, Dao-Rong. Atoms in lattice of radical classes of lattice-ordered groups. Archivum mathematicum, Tome 29 (1993) no. 3-4, pp. 221-226. http://geodesic.mathdoc.fr/item/ARM_1993_29_3-4_a10/

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