Pseudo Semiprojective I-covers And Strongly Dual ?-Rickart Module

The notion of pseudo semiprojective I-covers is introduced in Section 1.It is shown that every left R-module has a pseudo semiprojective I-cover if and only if every left R-module has a projective I-cover.It is also proved that the class of all pseudo semiprojective modules is a projectivity class,and then I-semiregular and I-semiperfect rings are characterized by pseudo semiprojective I-covers and some well known results are generalized.The concept of strongly dual ?-Rickart modules is introduced and its properties are studied in Section 2.The relations among strongly dual ?-Rickart modules and strongly dual Rickart modules,dual ?-Rickart modules are discussed,and strongly ?-regular rings are characterized by strongly dual ?-Rickart modules.