On the primefulness of local cohomology modules

Abstract

Let  be  a commutative Noetherian ring  with identity  For a non-zero module . We prove that a multiplication primeful module  and  are  I-cofinite  and primeful, for each  where    is an ideal of  with   . As a consequence, we deduce that,  if   and  are multiplication  primeful R- modules,  then  is primeful. Another result is, for  a projective  module  over an integral domain,   admits  projective resolution  such that each  is primeful (faithfully flat).