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Keywords:
lattice-ordered group; radical class; closure operator; atom
lattice-ordered group; radical class; closure operator; atom
Summary:
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.
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