Let R be a ring. Azumaya generalized the concept of projectivity of modules to single projectivity. The paper( Zhu S L. J Algebra,1991,139: 255- 261.) argued about rings over which every flat module is finitely projective. And the paper( Mao L X. Taiwanese J Math,2007( 12) : 501- 512.) gave a condition when every injective R-module is singly projective. This article shows some other relations between singly projective R-modules and other kinds of modules,such as quasi-injective R-modules,singly flat R-modules,finitely projective R-modules and divisible R-modules. And it is proved that singly projective modules are closed under direct sums.
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