Abstract
AbstractThe essential coverMkof a classMis defined as the class of all essential extensions of rings belonging toM.Mis called essentially closed ifMk=M. Every classMhas a unique essential closure, i.e. a smallest essentially closed class containingM.LetMbe a hereditary class of (semi)prime rings. ThenMis proved to be a (weakly) special class if and only ifMis essentially closed. A main result is thatMkis the smallest (weakly) special class containingM. Further it is shown that the upper radicalUMdetermined byM, is hereditary if and only ifUMhas the intersection property with respect toMk.
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