中文摘要：

模M称为P-投射模,是指对任意R-模N的任意循环子模Rx,同态f：M→N/Rx能提升为同态g：M→N.给出了P-投射模的一些新刻划,证明了M是P-投射模当且仅当对任何有限生成模K有Ext1R（M,K）=0当且仅当对R的任何左理想I有Ext1R（M,R/I）=0.并利用P-投射性与f-内射性给出了半单环的新刻划,证明了R是半单环当且仅当每个模是P-投射模当且仅当每个模是f-内射模.最后为了进一步揭示P-投射模的子模的性质,引入了P-遗传环的概念,证明了R是P-遗传环当且仅当有限生成模的内射维数不超过1.

英文摘要：

A module M is called P-projective,if for any cyclic submodule Rx of any module N,every homomorphism f： M→N / Rx can be extended to a homomorphism g： M→N.In this paper,the new equivalent definitions of the P-projective module are shown.For example,M is P-projective if and only if Ext1R（M,K） =0 for every finite generated K,if and only if Ext1R（M,R/I） =0 for any idea I of the ring R.Then the semisimple ring is charactered by P-projective modules and f-injective modules.For instance,R is semisimple if and only if every R-module is P-projective if and only if every R-module is f-injective.Finally,in order to discuss the properties of the submoudules of P-projective modules,the definition of the P-hereditary ring is described.It is proved that R is P-hereditary if and only if the injective dimension of the finitely generated module is less than 1.