关于乘法模的弱准素子模

摘要

讨论了乘法模的弱准素子模的性质.并证明了设R是具有单位元的交换环,M是酉R-模.(1)如果M是乘法模,N是M的弱准素子模,则√N是M的素子模;(2)设M是乘法模,L是M的子模,f:M-L是满同态.如果N是L的弱准素子模,则f-1(N)是M的弱准素子模.%The properties of weak primary submodules of multiplication modules are studied. It is shown that:Let R be a commutative ring with identity and M a unitary R-module. (1)If M is a multiplication Module and N is a weak primary submodule of M,then (√)N is a prime submodule of M; (2)Let M be a multiplication module,L a submodule of M and f : M→L an epimorphism. If N is a weak primary submodule of L,then f-1 (N) is a weak primary submodule of M.