a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

Let be a commutative ring with 1 and left unitary . In this papers we introduced studied concept P-small compressible (An is said to if can embedded in every of it nonzero submodule Equivalently, there exists monomorphism , retractable for non-zero homomorphism whenever as generalization respectively give some their advantages characterizations examples.

Our new meeting room, the MR Square, was built as a testing ground of a variety of multimedia user interfaces and applications. The MR Square features mixed-reality technologies such as wide-area trackers and tens of head mount displays, as well as one 200-inch and two 150-inch screens. Participants sit and collaborate in fully wired, retractable seats. The MR Square illustrates how state of th...