On a theorem of kulikov for artinian rings

Abstract

For a right artinian Ring A maximal submodules of pure projective right A-modules (i.e. of direct sums of modules of finite length) are again pure projective if and only if the category of finitely generated right A-modules is right noetherian, equivalently, if right glob. dim . In this case pure projectivity generally is hereditary in Mod-A (Kulikov-property). The Kulikov-property can be tested by generalized almost split sequences, the test also works in the case of Oedekind domains.