2

Some results on strongly prime submodules

كارشناسي ارشد

رياضي

دانشگاه پيام نور شاهرود

1395

دكتر بوجاري

Abstract Let R be a commutative ring with identity and let M be an R-module. A proper submodule P of M is called strongly prime submodule if (P + Rx : M ) y ⊆ P for x, y ∈ M , implies that x ∈P or y ∈ P . It is shown that a finitely generated R-module M is Artinian if and only if M is Noetherian and every strongly prime submodule of M is maximal. We also study the strongly dimension of a module which is defined to be the length of a longest chain of strongly prime submodules. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of prime ideal. In particular, the Generalized Principal Ideal Theorem is extended to modules.

62668