关于M-(m,n)-内射性

On M-(m,n)-injectivity

设R是一个环.一个右R-模N叫做M-(m,n)-内射的,如果每一个从Rm的n-生成子模到N的右R-模单同态都能扩展到Rm到N的R-模同态.如果RR是M-(m,n)-内射的,则称R是右M-(m,n)-内射的.M-(m,n)-内射性是MP-内射性的推广.本文首先给出了一个右R-模N是M-(m,n)-内射模的刻画,其次通过MP-内射性给出了N是M-(m,n)-内射的一个充分条件,最后给出了可裂零扩张是M-(m,n)-内射的一个性质,从而推广了MP-内射性的性质.

Let Rbe a ring.A right R-module Nis called M-（m,n）-injective,if every right R-monomorphism from an n-generated submodule of Rmto Nextends to one fromRmto N.If RRis right M-（m,n）-injective,then Ris called a right M-（m,n）-injective ring.It is obvious that M-（m,n）-injectivity is a generalization of MP-injectivity.In this paper,firsrtly,the authors give some characterizations on M-（m,n）-injectivity;secondly,it gives a sufficient condition that Nis M-（m,n）-injective by MP-injectivity;finally,the authors give a property on the split null extension which is M-（m,n）-injectivite.Some results generalize the properties on MP-injectivity.