A Characterization of Semihereditary Radicals

Abstract:

      In this paper, it is proved that a radical is semihereditary if and only if its subdirectly irreducible semisimple class is seminormal. It is shown that the inter-section radical of semihereditary radicals is also semihereditary. The construc-tion of lower radical is given for the smallerst hereditary radical and semihe-reditary radical with the subdirectly irreducible semisimple class K