2型X-extending模与Osofsky-Smith定理

Type 2 X-extending modules and Osofsky-Smith Theorem

设 R是有单位元的环 ,X是所有半单左 R-模及 singular左 R-模构成的模类 ,M是循环的extending左 R-模 .本文证明了若 M的所有循环子商都是 2型 X- extending模 ,则 M具有有限一致维数 .该结果推广了著名的 Osofsky- Smith定理 .

Let R be a ring with identity,and X be the module class consists of all semisimple and all singular left R-modules.For a cyclic extending left R-module M,we show that if all cyclic subfactors of M are type 2 X-extending,then M has finite uniform dimension.This result is a generalization of Osofsky-Smith Theorem.