关于拟WGP-内射模

On Quasi WGP-injective Mdules

定义了拟WGP-内射模,给出了拟WGP-内射模的一些刻画及性质。设R为环,M是右R-模,S=End(M),证明了MR是一个右拟WGP-内射模当且仅当对于任意的0≠a∈S,存在0≠c∈S,使得ac≠0且lS(ker(ac))=Sac;设M是右拟WGP-内射的自生成子,S半素,则S的每个极大核是M的直和项;设MR是右拟WGP-内射模,对于S的任意右一致元u,Au={s∈S|kers∩u(M)≠0}是包含ls(u(M))的一个极大左理想,从而推广了WGP-内射环的一些结果。

Abstract： Quasi WGP - injective modules are defined. Then some characterizations and properties are given. Let R be a ring, M right R - module, S = End（ MR ） . It is shown that M is a right quasi WGP - injective module if and only if for and 0≠a ∈ S, there exists 0 ≠ c∈ S such that 1s （ ker（ac） ） = Sac. Moreover, it is proved that if M is a right quasi WGP - injective self - genera- tor and S is a semiprime ring, then every maximal kernel of S is a summand of M ; If M is a right quasi WGP - injeetive module, then for any right uniform dement of S, the set Au = { s ∈ S I kers ∩ u （M）≠ 0 } is a maximal left ideal of S containing ls （ u （M））. Consequently, some results of WGP- injective rings are generalized.