ON SEMIPRIME MODULES WITH CHAIN CONDITIONS

K. F. U. Ahmed, Le Phuong Thao, Nguyen V. Sanh

Abstract


Let R be an arbitrary ring, M a right R-module and S=End_R(M), the
endomorphism ring of M. A proper fully invariant submodule X of M
is called a prime submodule of M if for any ideal I of S and any fully
invariant submodule U of M, if I(U) \subset X, then either I(M) \subset X or
U \subset X. A submodule X of M is called a semiprime submodule of M
if it is an intersection of prime submodules. The module M is called a
prime module if 0 is a prime submodule of M, and semiprime if 0 is a
semiprime submodule of M. In this paper, we present some results on
the classes of semiprime modules with chain conditions.

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