Torsion classes and radical classes of lattice ordered groups have been investigated in several papers. The notions of torsion class and of radical class of generalized Boolean algebras are defined analogously. We denote by T g and R g the collections of all torsion classes or of all radical classes of generalized Boolean algebras, respectively. Both T g and R g are partially ordered by the class-theoretical inclusion. We deal with the relation between these partially ordered collection; as a consequence, we obtain that T g is a Brouwerian lattice. W. C. Holland proved that each variety of lattice ordered groups is a torsion class. We show that an analogous result is valid for generalized Boolean algebras.
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机译：几篇论文研究了晶格有序基团的扭转类别和自由基类别。广义布尔代数的扭转类和根类的概念被类似地定义。我们用T g和R g分别表示广义布尔代数的所有扭转类或所有根类的集合。 T g和R g均由类理论包含部分排序。我们处理这些部分有序集合之间的关系;结果，我们得到T g是Brouwerian晶格。 W. C. Holland证明，每一种晶格有序组都是一个扭转类。我们证明了相似的结果对于广义布尔代数是有效的。
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