Right orthogonal class of pure projective modules over pure hereditary rings

Abstract

We consider the class of all pure projective modules. Present article we investigate the right orthogonal class of all pure projective modules and these modules are defined via the vanishing cohomology of pure projective modules. We discuss the existence of preenvelope and the coresolution of these modules. Further, we show that the right orthogonal class of all pure projective modules is coresolving (injectively resolving) over a pure-hereditary ring and we analyze the dimensions of these modules. Finally, we proved the desirable properties of the dimension when the ring is semisimple artinian.