SOME RESULTS ON STRONGLY PRIME SUBMODULES

Let r be a commutative ring with identity and let mbe an r-module. a proper submodule p of m is called stronglyprime submodule if (p +rx : m)y  p for x; y 2 m, implies thatx 2 p or y 2 p. it is shown that a nitely generated r-module mis artinian if and only if m is noetherian and every strongly primesubmodule of m is maximal. we also study the strongly dimensionof a module which is dened to be the length of a longest chain ofstrongly prime submodules.