[PDF][PDF] On prime and semiprime submodules of multiplication modules
R Jahani-Nezhad, MH Naderi - International Mathematical Forum, 2009 - m-hikari.com
International Mathematical Forum, 2009•m-hikari.com
Let R be a commutative ring. An R-module M is called a multiplication module if for each
submodule N of M, N= IM, for some ideal I of R. In this paper, first we define the notion of
residual of a submodule in M and then we obtain some related results. In particular, we state
and prove some equivalent conditions for prime and semiprime submodules of a
multiplication module.
submodule N of M, N= IM, for some ideal I of R. In this paper, first we define the notion of
residual of a submodule in M and then we obtain some related results. In particular, we state
and prove some equivalent conditions for prime and semiprime submodules of a
multiplication module.
Abstract
Let R be a commutative ring. An R-module M is called a multiplication module if for each submodule N of M, N= IM, for some ideal I of R. In this paper, first we define the notion of residual of a submodule in M and then we obtain some related results. In particular, we state and prove some equivalent conditions for prime and semiprime submodules of a multiplication module.
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