Weak Projective Modules And Complexes

In the paper,we introduce and study weak projective modules and weak projec-tive complexes.We show that the class of weak projective modules strictly contained in the class of FP-projective modules;when the ring is coherent,the class of weak projective modules in accordance with the class of FP-projective modules.We show that the cotorion pair(WP,WI)is complete and hereditary,where WP is the class of weak projective modules and WI is the class of weak injective modules.At the same time,we give some homological characterizations of weak projective com-plexes,prove the class of weak projective complexes is closed under extensions and direct sums.We prove if C is a weak projective complex,then the module Cn is weak projective;if C is a weak projective module,then the complex C[n]is weak projective.