MMN-4569
Relatively hereditary radical classes of rings
Elena Cojuhari; Barry Gardner;Abstract
Radical classes of rings are studied which, while not hereditary, are closed with respect to ideals of some kind: maximal, prime and finite index ideals among others. In some, but not all cases, the ideal property is characterized by the corresponding class of factor rings; for instance maximal ideals correspond to simple rings. Such characterizations sometimes make it possible to prove results for several types of ideals simultaneously. Several results for hereditary radicals are generalized to various types of relatively hereditary ones; e.g. if $\mathcal{R}$ is hereditary then for $I\triangleleft A$ we have $\mathcal{R}(I)=I\cap \mathcal{R}(A)$ and hereditary classes define hereditary lower radical classes. In the construction of examples, use is made of A-radical classes and this leads to some consideration of radical classes of abelian groups.
Vol. 26 (2025), No. 1, pp. 163-179