I-提升模的有限直和

摘要

As is well known, the finite direct sums of I-lifting modules may not be I-lifting modules. In this paper, we give some conditions such that finite direct sums of I-lifting modules are still I-lifting modules. Namely, we prove that when M =M1⊕M2, where M1 and M2 are I-lifting. If Mi is Mj-projective (i, j=1, 2) or M is a duomodule, then M is I-lifting.%　　I-提升模的直和不一定是I-提升模。本文给出了使I-提升模的直和仍是I-提升模成立的条件,即证明了当M =M1⊕M 2,其中M1和M2是I-提升的。如果Mi是Mj-投射的(i, j=1,2)或M 是duo模,则M 是I-提升的。