On the module of homomorphisms into projective modules and multiplication modules

On y-closed Rickart Modules

“…Definition 2.1: Let and be two -modules. We say that is -y-closed Rickart module if for each ( ) ( ) is a y-closed submodule of For a module , if is -y-closed Rickart module, then we say that is y- ( ) is a commutative and hence is a multiplication [7]. Proposition 3.9: Let be an -module with the property that the intersection of any two yclosed submodules of is a y-closed submodule of .…”

On Rickart Modules

“…, is a p.p. is a commutative and hence is multipliction [8] Recall that an -module is called an SIP module if the intersection of any two direct summands of is also a direct summand of [9]. It is known that every Rickart module is an SIP module [1].…”